how much electricity will solar panels produce

Understanding the electricity output of solar panels is crucial for homeowners, business owners, and energy investors considering a photovoltaic (PV) system. The amount of power generated by a solar array is not a fixed number; it depends on a complex interplay of geographical, technical, and environmental factors. This guide breaks down the science of solar production, provides realistic output estimates, and offers actionable insights to maximize your return on investment. By the end of this article, you will have a clear framework to calculate potential generation for your specific location and system design.

1. The Core Formula: Calculating Solar Panel Output

At its most basic level, the electricity produced by a solar panel is calculated using a simple formula: System Size (kW) × Peak Sun Hours (PSH) × Performance Ratio (PR). However, each of these variables carries significant weight and complexity. The system size refers to the rated capacity of the panels under standard test conditions (STC), typically measured in kilowatts (kW). Peak sun hours are not the total daylight hours, but rather the equivalent number of hours per day when solar irradiance averages 1,000 watts per square meter. The performance ratio accounts for real-world losses such as inverter inefficiency, wiring resistance, soiling, and thermal losses.

For example, a 5 kW system in a location receiving 4.5 peak sun hours with a performance ratio of 0.80 would produce approximately 18 kWh per day (5 × 4.5 × 0.80). This baseline calculation is essential, but it is only the starting point. Let’s dissect each factor in detail to understand how they influence your specific output.

1.1 System Size: Rated Capacity vs. Real-World Power

The rated capacity of a solar panel, expressed in watts (W), is determined under laboratory conditions at 25°C (77°F) with 1,000 W/m² of irradiance. A typical residential panel today ranges from 400W to 500W. However, this rating does not reflect actual operating conditions. When panels heat up above 25°C, their efficiency drops. This is known as the temperature coefficient, usually around -0.3% to -0.5% per degree Celsius. In hot climates, a 400W panel might only produce 350W during peak heat. Therefore, the “nameplate” capacity is a theoretical maximum, not a continuous output.

1.2 Peak Sun Hours: The Geographic Variable

Peak sun hours (PSH) vary dramatically by location, season, and weather patterns. A location in Arizona might receive 6.5 PSH in June but only 3.5 PSH in December. Conversely, Seattle might average only 2.5 PSH in winter. This is why the same 5 kW system can produce 30 kWh/day in one state and 15 kWh/day in another. You can find PSH data for your specific city from sources like the National Renewable Energy Laboratory (NREL) or the Global Solar Atlas. It is critical to use annual average PSH for budgeting, but monthly data is better for understanding seasonal fluctuations.

1.3 Performance Ratio: Accounting for Real-World Losses

The performance ratio (PR) is a dimensionless number that represents the efficiency of the entire system after all losses. A modern, well-designed system will have a PR between 0.75 and 0.85. Losses come from several sources:

Inverter losses: Converting DC to AC typically loses 3-8% of energy.
Temperature losses: Heat reduces panel voltage, causing a 5-10% loss in hot climates.
Soiling and dirt: Dust, bird droppings, and pollen can reduce output by 2-5% if not cleaned regularly.
Shading: Even partial shade from a chimney or tree can disproportionately reduce output due to series wiring.
Wiring and connection losses: Resistance in cables accounts for 1-2% loss.

2. Average Daily and Monthly Output by System Size

To provide a practical reference, the table below illustrates estimated daily electricity production for common residential system sizes across different peak sun hour scenarios. These figures assume a performance ratio of 0.80, which is typical for a well-installed system.

System Size (kW)	Low PSH (3.0 hrs)	Average PSH (4.5 hrs)	High PSH (6.0 hrs)	Annual Output (Avg PSH)
3 kW	7.2 kWh/day	10.8 kWh/day	14.4 kWh/day	3,942 kWh/year
5 kW	12.0 kWh/day	18.0 kWh/day	24.0 kWh/day	6,570 kWh/year
7 kW	16.8 kWh/day	25.2 kWh/day	33.6 kWh/day	9,198 kWh/year
10 kW	24.0 kWh/day	36.0 kWh/day	48.0 kWh/day	13,140 kWh/year
15 kW	36.0 kWh/day	54.0 kWh/day	72.0 kWh/day	19,710 kWh/year

These numbers are estimates. For precise figures, you must consult a solar installer who can run a site-specific simulation using tools like Helioscope or Aurora. However, this table gives you a ballpark for energy budgeting. For instance, the average U.S. home consumes about 10,800 kWh annually. A 7 kW system in an average location would nearly cover that demand.

3. The Impact of Panel Type on Electricity Generation

Not all solar panels are created equal. The technology and efficiency of the photovoltaic cells directly influence how much electricity a given area of roof can produce. There are three main types of panels available on the market today, each with distinct performance characteristics.

3.1 Monocrystalline Panels (Mono-SI)

These are the most efficient and popular panels for residential use. Made from single-crystal silicon, they have an efficiency range of 17% to 22%. This means they convert a higher percentage of sunlight into electricity. For a given physical size, a mono panel will produce more watts than a poly panel. They also perform slightly better in high temperatures and low-light conditions. The trade-off is a higher upfront cost per watt.

3.2 Polycrystalline Panels (Poly-SI)

Poly panels are made from fragments of silicon crystals melted together. They have a lower efficiency, typically 15% to 17%. This means you need more roof space to achieve the same output as a mono system. However, they are cheaper to manufacture, making them a budget-friendly option. In terms of electricity output, a 5 kW poly system will produce the same annual kWh as a 5 kW mono system, but the poly system will occupy a larger physical area.

3.3 Thin-Film Panels

Thin-film panels are lightweight and flexible, but their efficiency is significantly lower, ranging from 10% to 13%. They require substantial roof space, making them less common for residential rooftops. However, they perform better in high heat and diffuse light. For large-scale industrial projects with vast land availability, they can be cost-effective. For a residential context, they are generally not recommended unless roof weight is a structural concern.

The table below summarizes the typical output per square meter for each panel type under standard test conditions.

Panel Type	Efficiency (%)	Watts per m²	Relative Cost per Watt
Monocrystalline	18-22%	180-220 W/m²	High
Polycrystalline	15-17%	150-170 W/m²	Medium
Thin-Film	10-13%	100-130 W/m²	Low

4. How Location and Climate Affect Solar Electricity Production

Your geographic location is the single most significant determinant of solar output. The amount of solar radiation reaching your panels is influenced by latitude, altitude, and local weather patterns. However, it is not just about sunshine; temperature and air quality also play critical roles.

4.1 Solar Irradiance and Latitude

Areas closer to the equator receive more direct sunlight year-round, leading to higher peak sun hours. For example, a system in Southern California (latitude 34°N) will produce roughly 30% more electricity than the same system in Northern Germany (latitude 52°N). In the United States, the Southwest (Arizona, Nevada, New Mexico) has the highest solar resource, while the Pacific Northwest and parts of the Northeast have significantly lower irradiance.

4.2 Temperature and Thermal Degradation

Contrary to popular belief, solar panels prefer cooler temperatures. While they need sunlight, excessive heat reduces their efficiency. A panel rated at 400W will produce less than 400W when the ambient temperature exceeds 25°C. For every 10°C increase above 25°C, output can drop by 3-5%. This means a hot, sunny day in Phoenix might actually yield less electricity per panel than a cool, sunny day in Denver. This is why the performance ratio is critical in hot climates.

4.3 Air Quality and Pollution

Airborne particulates and smog can scatter and absorb sunlight, reducing the irradiance reaching the panel surface. Urban areas with high pollution levels may experience a 5-10% reduction in potential output compared to rural areas with clean air. Additionally, panels in dusty environments require more frequent cleaning to maintain optimal performance.

5. Seasonal Variations in Solar Panel Electricity Output

Solar production is not constant throughout the year. The tilt of the Earth’s axis causes the sun’s path to change, affecting both the duration and intensity of sunlight. Understanding these seasonal patterns is essential for managing energy expectations, especially for off-grid or battery-backed systems.

5.1 Summer vs. Winter Production

In the Northern Hemisphere, the summer solstice (June 21) provides the longest day and the highest solar elevation angle, resulting in maximum production. Conversely, the winter solstice (December 21) offers the shortest day and lowest sun angle, leading to minimal output. For example, a system in New York might produce 45 kWh/day in June but only 15 kWh/day in December. This 3:1 ratio is common in mid-latitude regions.

5.2 The Impact of Snow and Ice

Snow can be a double-edged sword. A heavy snow cover will completely block sunlight, halting production. However, snow also reflects light (albedo effect), which can increase production on clear days following a snowfall if the panels are tilted. Most modern panels are installed at an angle that allows snow to slide off, but this is not always immediate. In snowy climates, you should budget for several days of zero production during major storms.

5.3 Cloud Cover and Diffuse Light

Even on cloudy days, solar panels produce electricity, albeit at a reduced rate. Diffuse light from clouds can still generate 10-25% of the panel’s rated capacity. The exact output depends on cloud thickness. A thick, overcast sky might yield 5% output, while thin, wispy clouds might yield 40%. Therefore, seasonal weather patterns, such as monsoon seasons or persistent fog, will significantly affect monthly totals.

6. Roof Orientation and Tilt Angle: Maximizing Your Yield

The physical orientation of your solar array has a direct and quantifiable impact on electricity generation. To capture the maximum amount of sunlight, panels should ideally face the equator. In the Northern Hemisphere, this means true south (not magnetic south). The optimal tilt angle is approximately equal to your latitude.

6.1 Azimuth (Direction)

South-facing panels (azimuth of 180°) in the Northern Hemisphere will produce the highest annual output. However, east and west-facing panels can still be viable, especially in regions with time-of-use electricity rates. East-facing panels generate more power in the morning, while west-facing panels generate more in the afternoon. This can be strategically beneficial for homeowners who consume more electricity in the evening. The table below shows the relative output loss for different orientations compared to a perfect south-facing array.

Orientation	Relative Output (vs. South)	Best Time of Day
South (180°)	100%	Midday
South-West (225°)	94-97%	Late Afternoon
South-East (135°)	94-97%	Late Morning
West (270°)	85-90%	Late Afternoon
East (90°)	85-90%	Late Morning
North (0°)	65-75%	Midday (low intensity)

6.2 Tilt Angle

The tilt angle (elevation) of the panels should be adjusted to optimize for seasonal production. A tilt angle equal to your latitude maximizes annual output. If you tilt the panels lower (closer to horizontal), you will produce more in summer but less in winter. If you tilt them steeper, you will produce more in winter but less in summer. For net metering scenarios where annual production is what matters, latitude tilt is best. For off-grid systems with heavy winter loads, a steeper tilt is often recommended to capture low-angle winter sun.

6.3 Solar Trackers

For ground-mounted systems, solar trackers can be used to follow the sun’s path across the sky. Single-axis trackers increase output by 15-25%, while dual-axis trackers can increase it by 25-35%. However, trackers add significant upfront cost and require more maintenance due to moving parts. They are generally not cost-effective for residential systems unless you have ample land and high electricity prices.

7. Estimating Your Home’s Specific Solar Electricity Production

To move from general estimates to a precise calculation for your property, you need to follow a systematic process. This involves gathering specific data about your location, roof, and energy consumption. Here is a step-by-step guide to estimating your potential solar output.

7.1 Step 1: Determine Your Roof’s Usable Area

Measure the dimensions of your roof. Exclude areas with chimneys, skylights, vents, or significant shading. A standard 400W panel measures approximately 1.7 meters by 1.1 meters (about 1.87 m²). You can typically fit about 2 panels per 4 square meters of roof space, accounting for spacing and access requirements. Calculate the total usable square meters and divide by 1.87 to get the maximum number of panels you can install.

7.2 Step 2: Find Your Peak Sun Hours

Use the NREL PVWatts calculator or the Global Solar Atlas. Enter your address to get the annual average PSH. For example, let’s say you live in Dallas, Texas. The annual average PSH is approximately 4.8 hours per day. This number is already adjusted for typical weather patterns and atmospheric effects.

7.3 Step 3: Calculate Gross Output

Multiply the total system size (number of panels × wattage) by the PSH. For instance, if you can fit 20 panels of 400W each, your system size is 8 kW. The gross daily output would be 8 kW × 4.8 PSH = 38.4 kWh/day. This is the theoretical maximum before losses.

7.4 Step 4: Apply Performance Ratio

Multiply the gross output by the performance ratio. Using a conservative PR of 0.78, your net daily output would be 38.4 × 0.78 = 29.95 kWh/day. Annually, this equates to approximately 10,932 kWh. This is a realistic estimate of what your system will produce.

7.5 Step 5: Compare with Your Consumption

Review your past 12 months of electricity bills to find your average daily consumption. If you use 30 kWh/day, this 8 kW system would cover 99% of your needs. If you use 40 kWh/day, you would only cover 75% and may need to expand the system or reduce consumption.

8. Advanced Considerations: Inverter Clipping, Degradation, and Battery Storage

Beyond the basic calculations, several advanced factors can influence the actual electricity you see from your solar panels. These include the inverter’s DC-to-AC ratio, the gradual degradation of panel efficiency over time, and the integration of battery storage.

8.1 Inverter Clipping and DC/AC Ratio

Inverters have a maximum AC output rating. If your solar array’s DC capacity is significantly higher than the inverter’s AC capacity, the inverter will “clip” or limit the output during peak sun hours. This is a deliberate design choice to reduce inverter cost. A typical DC/AC ratio is 1.1 to 1.3. For example, a 6.5 kW DC array might be paired with a 5 kW AC inverter. During the few hours of peak sun, the inverter will cap output at 5 kW, wasting a small amount of potential energy. However, this wasted energy is often negligible (1-3% annually) and is offset by the lower cost of a smaller inverter.

8.2 Panel Degradation Over Time

Solar panels do not last forever at full capacity. They degrade at a rate of about 0.5% to 0.8% per year. This means a panel rated at 400W will produce 398W in year two, 396W in year three, and so on. Most reputable manufacturers offer a performance warranty guaranteeing at least 80% output after 25 years. When calculating long-term financial returns, you should factor in this degradation. Over a 25-year period, the average annual output will be roughly 90% of the year-one output.

8.3 Battery Storage and Self-Consumption

Adding a battery storage system changes how you measure solar production. Without a battery, excess electricity is exported to the grid (often at a lower rate than you pay for imports). With a battery, you can store excess daytime production for evening use. This increases your self-consumption ratio, which is the percentage of solar energy you use directly. While batteries do not increase the total electricity produced, they increase the economic value of that electricity by reducing the amount you draw from the grid during peak rate periods. However, batteries also have round-trip efficiency losses of about 10-15%, meaning you lose some energy in the charge/discharge cycle.

8.4 Monitoring and Maintenance

To ensure your system produces the expected amount of electricity, you should install a monitoring system. Most modern inverters come with Wi-Fi connectivity and apps that show real-time and historical production data. Regularly compare your actual production to the estimated production from your initial design. If you notice a significant drop (more than 10%), it may indicate a fault, soiling, or shading issue. Cleaning panels 1-2 times per year, especially in dry or dusty climates, will help maintain optimal output.

Frequently Asked Questions (FAQ)

1. How many kWh per day does a 5 kW solar system produce?

A 5 kW system will produce between 12 kWh and 24 kWh per day, depending on your location and system efficiency. In an average U.S. location with 4.5 peak sun hours and a performance ratio of 0.80, it will produce approximately 18 kWh per day.

2. Do solar panels work on cloudy days?

Yes, solar panels still produce electricity on cloudy days, but at a reduced rate. They typically generate 10-25% of their rated capacity under heavy cloud cover, and up to 40% under thin clouds. The exact output depends on the thickness and density of the clouds.

3. How much electricity does a 100-watt solar panel produce?

A 100W panel produces about 300-500 watt-hours (0.3-0.5 kWh) per day, depending on peak sun hours. In a location with 4.5 PSH and a 0.80 PR, it would produce 360 Wh per day (100 × 4.5 × 0.80).

4. What is the average annual output of a 6 kW system?

A 6 kW system produces approximately 8,000 to 10,000 kWh per year in most U.S. locations. In sunny states like California or Arizona, it can reach 11,000 kWh, while in cloudy states like Washington, it may be closer to 7,000 kWh.

5. How long do solar panels take to pay for themselves?

The payback period typically ranges from 6 to 12 years, depending on your electricity rates, available incentives, and system cost. After the payback period, the electricity generated is essentially free, aside from minimal maintenance costs.

6. Does roof orientation significantly affect output?

Yes. A south-facing roof in the Northern Hemisphere is optimal. East or west-facing roofs will produce 10-15% less electricity. A north-facing roof will produce 25-35% less. However, with modern high-efficiency panels, even east/west orientations can be economically viable.

7. How much roof space do I need for a 10 kW system?

A 10 kW system typically requires about 600-700 square feet of unobstructed roof space. This is based on using 400W panels that measure about 21 square feet each. You would need approximately 25 panels.

8. What is the performance ratio in solar systems?

The performance ratio (PR) is a measure of the system’s actual output compared to its theoretical maximum output. It accounts for all losses, including inverter inefficiency, temperature, wiring, and soiling. A good PR is between 0.75 and 0.85.

9. Does panel temperature affect electricity production?

Yes, solar panels lose efficiency as they heat up. For every 1°C above 25°C, a typical panel loses 0.3% to 0.5% of its output. On a 40°C day, a panel could lose 5-8% efficiency compared to standard test conditions.

10. Can I generate enough solar power to run my entire house?

Yes, it is entirely possible. You need to size your system to match your annual consumption. If your home uses 12,000 kWh per year, you would need a system rated at approximately 9-10 kW in an average location. A professional installer can design a system to cover 100% of your usage.

Market Pain Points and Solutions in Solar Electricity Generation

The solar industry faces several significant challenges that affect how much electricity systems actually produce and how satisfied customers are with their investments. Understanding these pain points is essential for anyone considering a solar installation.

Pain Point 1: The “Estimate vs. Actual” Discrepancy

Problem: Many homeowners are disappointed when their actual production is lower than the salesperson’s estimate. This often happens because initial estimates use overly optimistic peak sun hours or ignore shading and temperature losses. A sales estimate might assume a PR of 0.85, but the real-world system only achieves 0.70 due to poor installation or micro-shading.

Solution: Demand a detailed proposal that includes a site-specific simulation using software like Helioscope or Aurora. Ask for a production guarantee or performance warranty. Install monitoring to track real-time output. If a system underperforms by more than 10% against the simulation, the installer should diagnose and fix the issue under warranty.

Pain Point 2: Shading from Trees and Neighboring Buildings

Problem: Even a small amount of shade on a single panel can reduce the output of an entire string of panels due to series wiring. This is known as the “Christmas light effect.” A tree that casts a shadow on just 5% of a roof can reduce total system output by 20-30%.

Solution: Use microinverters or power optimizers instead of a single string inverter. These devices allow each panel to operate independently, so shading on one panel does not affect others. Additionally, consider trimming or removing trees that cause shading, or design the system to avoid shaded areas entirely. A professional site assessment should use a tool like Solmetric SunEye to map shade patterns throughout the year.

Pain Point 3: Roof Orientation and Space Constraints

Problem: Not all roofs are perfectly oriented. Many homeowners have east-west facing roofs, which reduces output. Others have limited usable space due to obstructions, making it impossible to install a system large enough to cover their energy needs.

Solution: For east-west roofs, install a higher number of lower-wattage panels to maximize the use of available space. Alternatively, use higher-efficiency monocrystalline panels (like those from SunPower or REC) to generate more watts per square foot. If roof space is insufficient, consider a ground-mounted system in the yard, which allows for optimal tilt and orientation without structural constraints.

Pain Point 4: Degradation and Long-Term Performance

Problem: All solar panels degrade over time, but the rate varies significantly between manufacturers. Some low-quality panels may degrade at 1% per year, meaning they lose 25% of their capacity over 25 years. This reduces long-term electricity production and financial returns.

Solution: Purchase panels from Tier 1 manufacturers with strong performance warranties. Look for panels with a degradation rate of 0.5% or lower per year. Review the warranty terms carefully; a good warranty guarantees at least 90% output after 10 years and 80% after 25 years. Investing in premium panels may cost more upfront but ensures higher output over the system’s lifetime.

Pain Point 5: Inverter Failures and Downtime

Problem: The inverter is the most likely component to fail in a solar system. A typical string inverter has a lifespan of 10-15 years, while panels last 25-30 years. When an inverter fails, the entire system stops producing electricity until it is replaced, leading to significant lost production.

Solution: Choose microinverters or power optimizers, which have a longer lifespan and offer panel-level monitoring. These systems are more expensive but reduce the risk of total system downtime. Alternatively, ensure your inverter warranty includes rapid replacement. Some manufacturers, like Enphase, offer a 25-year warranty on their microinverters, matching the panel warranty.

Pain Point 6: Net Metering Policy Changes

Problem: Many states and utilities are reducing or eliminating net metering, which pays solar owners retail rates for excess electricity exported to the grid. This reduces the financial value of solar production, especially for systems sized to produce more than the home consumes.

Solution: Adapt your system design to maximize self-consumption. This means sizing the system to cover only 80-100% of your annual usage rather than oversizing. Adding a battery storage system allows you to store excess daytime production for evening use, increasing self-consumption to 70-80% or higher. This makes you less vulnerable to low export rates and provides backup power during outages.

Pain Point 7: Cleaning and Maintenance Neglect

Problem: In dusty or polluted areas, panels can lose 5-10% of their output due to soiling. Many homeowners neglect cleaning, assuming rain will do the job. However, rain often leaves residue, and in dry climates, dust accumulates rapidly.

Solution: Schedule professional cleaning at least once a year, or twice a year if you live in a high-dust area. If your panels are easily accessible from the ground, you can clean them yourself with a hose and a soft brush. Monitor your production data; if you see a gradual decline that cannot be explained by weather, it is likely due to soiling.

Pain Point 8: High Upfront Cost and Financing Barriers

Problem: The initial cost of a solar system (typically $15,000 to $30,000 before incentives) is a major barrier for many homeowners. Even with the 30% federal tax credit, the upfront cash outlay is substantial.

Solution: Explore various financing options: solar loans with low interest rates, solar leases, or power purchase agreements (PPAs). While leases and PPAs often provide lower long-term savings, they require zero upfront cost. Additionally, many states offer rebates, performance-based incentives, or property tax exemptions that reduce the net cost. Calculate your payback period carefully to determine which financing method offers the best return.

Pain Point 9: Aesthetic Concerns and HOA Restrictions

Problem: Many homeowners associations (HOAs) have strict rules about the appearance of solar panels, and some homeowners dislike the look of rooftop arrays. This can delay or prevent installations.

Solution: Use building-integrated photovoltaics (BIPV) such as solar shingles (e.g., Tesla Solar Roof) which blend seamlessly with traditional roofing materials. Alternatively, install panels on the ground or on a carport to keep the roof clear. Before purchasing, check local solar access laws; many states have “solar rights” laws that override HOA restrictions on solar installations, but you must still comply with reasonable aesthetic guidelines.

Pain Point 10: Lack of Transparency in Quotes

Problem: Solar quotes are notoriously complex, with varying prices per watt, different equipment brands, and hidden fees. This makes it difficult for consumers to compare offers and know if they are getting a fair deal.

Solution: Always obtain at least three quotes from different installers. Ask for a detailed breakdown of costs: equipment costs, labor, permits, and margin. Compare the cost per watt (total system cost divided by system size in watts). A typical range is $2.50 to $3.50 per watt. Be wary of quotes significantly below this range, as they may use inferior equipment or poor installation practices. Use online marketplaces like EnergySage to get standardized quotes from vetted installers.

Conclusion: Maximizing Your Solar Electricity Production

Determining how much electricity your solar panels will produce is a multi-faceted question that requires careful analysis of your geographic location, roof characteristics, system design, and equipment quality. While the theoretical formula of system size × peak sun hours × performance ratio provides a baseline, real-world production is influenced by temperature, shading, inverter clipping, and long-term degradation. On average, a 5 kW system in the United States produces between 6,000 and 9,000 kWh annually, but this can vary by up to 50% depending on where you live and how your system is installed.

To ensure you get the maximum possible output, you must prioritize several key actions. First, conduct a professional site assessment to accurately measure your roof’s solar potential and identify any shading issues. Second, invest in high-efficiency panels and modern inverter technology, such as microinverters or power optimizers, to mitigate the impact of partial shading and component failures. Third, engage a reputable installer who uses advanced simulation software to provide a realistic production estimate, and insist on a performance guarantee. Fourth, commit to regular maintenance, including cleaning and monitoring, to ensure your system operates at peak efficiency for decades.

Finally, consider your long-term energy strategy. As net metering policies evolve and electricity rates fluctuate, adding battery storage can increase your energy independence and maximize the economic value of every kilowatt-hour your panels produce. Solar power is not just a short-term investment; it is a long-term commitment to sustainable energy. By understanding the variables that affect production and proactively managing them, you can confidently expect your solar array to deliver reliable, clean electricity for 25 years or more, significantly reducing your carbon footprint and energy bills.