Solar Sizing Formulas for Loads, Batteries and Inverters

Getting the numbers right is the foundation of any safe, reliable solar installation. Whether you are planning a small off-grid cabin, a backup power system, or a portable setup, a handful of straightforward formulas will help you size loads, batteries, inverters and wiring correctly. This article walks through each essential calculation, using worked examples drawn from authoritative sources, so you can apply them to your own project.

1. Daily energy consumption

The first step in sizing any solar system is knowing how much energy you use each day. The Virginia Cooperative Extension provides a simple formula for estimating an appliance’s daily energy consumption: (Wattage × Hours Used per Day) ÷ 1000 = Daily kilowatt‑hour (kWh) consumption. One kilowatt equals 1,000 Watts, so dividing by 1,000 converts watt‑hours into the kilowatt‑hours that appear on utility bills and battery specifications.

As an example, the extension’s guide calculates the annual energy use of a window fan: (200 Watts × 4 hours per day × 120 days per year) ÷ 1000 = 96 kWh per year. If you need the daily figure, simply omit the days multiplier: 200 W × 4 h ÷ 1000 = 0.8 kWh per day. For appliances that cycle on and off, such as refrigerators, the guide suggests dividing the total plugged‑in time by three to approximate the hours the compressor actually runs at its rated wattage. You can find more guidance on building a complete load list in our Energy Needs article.

2. Watts, kilowatts and watt‑hours

Before moving to other formulas, it helps to be clear about the difference between power and energy. The U.S. Energy Information Administration explains that electricity is measured in units of power called Watts. One kilowatt (kW) equals 1,000 Watts, and for very large amounts, megawatts (MW) and gigawatts (GW) are used. Power describes the rate at which electricity is being used at a specific moment.

Energy, on the other hand, is power used over time. The EIA states that one Watthour (Wh) is the energy of one Watt used for one hour. A 40‑Watt light bulb left on for five hours consumes 200 Wh, or 0.2 kWh. Utility companies bill in kilowatt‑hours, and battery capacity is often expressed in watt‑hours or amp‑hours. Understanding this distinction is key when you move between daily energy totals and instantaneous power demands. For a deeper look at these basics, visit Solar Electricity Basics.

3. Power, current and Ohm’s law

Once you know the power a device draws, you can calculate the current that will flow through your wiring. Victron’s Wiring Unlimited guide sets out the fundamental relationship: Power (P, in Watts) equals Voltage (V) multiplied by Current (I, in Amperes), or P = V × I. Rearranged, I = P ÷ V. This tells you how many amps a load will pull from a battery at a given voltage.

The guide gives a practical example: a 2,400‑Watt load connected to a 12‑Volt battery draws 2,400 ÷ 12 = 200 Amps. That same load on a 24‑Volt battery would draw only 100 Amps, and on a 48‑Volt battery just 50 Amps. This is why higher system voltages are common in larger installations: lower current means thinner, less expensive cables and fewer losses.

Ohm’s law, also explained in the Victron guide, describes the relationship between voltage, current and resistance: V = I × R. Every cable and connection has some resistance, and as current increases, the voltage dropped across that resistance grows. We will return to this in the voltage‑drop section. For help choosing the right conductors for your system, see Cables and Connectors and System Design.

4. Battery bank voltage and capacity

Batteries are often connected together to form a bank that meets the system’s voltage and storage needs. Victron’s Wiring Unlimited guide explains the two basic arrangements: connecting batteries in series increases the voltage while the amp‑hour capacity stays the same; connecting them in parallel keeps the voltage the same but adds the amp‑hour capacities together. For example, two 12‑Volt, 100‑Ah batteries wired in series give a 24‑Volt, 100‑Ah bank. The same two batteries in parallel give a 12‑Volt, 200‑Ah bank. A series‑parallel combination can raise both voltage and capacity.

To compare batteries of different voltages, it is useful to convert amp‑hours to watt‑hours. Because energy equals power multiplied by time, and power equals voltage times current, the energy stored in a battery is simply its amp‑hour rating multiplied by its nominal voltage: Watt‑hours = Amp‑hours × Volts. A 12‑V, 100‑Ah battery therefore stores about 1,200 Wh (1.2 kWh) of energy. This conversion helps you match battery capacity to your daily energy consumption.

Victron’s guide notes that large battery banks made from many paralleled 12‑V lead‑acid strings can become unbalanced due to slight differences in wiring resistance and battery internal resistance. For bigger banks, the guide points to alternatives such as 2‑Volt lead‑acid cells in series or lithium batteries with built‑in battery management systems. You can explore these options further in Batteries and Battery Sizing.

5. Inverter load: running watts and starting surge

An inverter must be sized to handle the total running wattage of all the AC devices that could operate at the same time. You can find the running wattage on the appliance’s nameplate or in the typical wattage table published by the Virginia Cooperative Extension. For example, the table lists a frost‑free 16‑cubic‑foot refrigerator at 725 Watts, a microwave oven at 750 to 1,100 Watts, and a laptop at about 50 Watts.

Motors present an additional challenge. The Virginia Cooperative Extension states that when measuring the current drawn by a motor, “the meter will show about three times more current in starting the motor than when it is running smoothly.” The extension calls this extra demand during starting part of a motor’s design. Check that your inverter’s surge rating can cover it: as a rough illustration, if a refrigerator runs at 725 W (about 6 A at 120 V), three times that current would be roughly 18 A at the moment of starting. When adding up loads, include the highest surge among the devices that might start together. For more on selecting the right inverter, see Inverters and Inverter Sizing.

6. Voltage drop and why it grows with current and cable length

Every cable has resistance, and when current flows through it, some voltage is lost along the way. Victron’s Wiring Unlimited guide provides the formula: Voltage drop = Current × Resistance. The resistance of a cable depends on its material, cross‑sectional area and length. The guide demonstrates this with a 2,400‑W inverter running from a 12‑V battery through two 1.5‑meter, 16‑mm² cables, each with a resistance of 1.6 milliohms (0.0016 Ω). At 200 A, the voltage drop across one cable is 200 × 0.0016 = 0.32 V. With both the positive and negative cables, the total drop is 0.64 V, so the inverter receives only 11.36 V instead of 12 V.

The same load at 24 V draws 100 A, giving a total drop of 0.32 V (1.3%), and at 48 V the drop falls to 0.16 V (0.3%). Victron recommends aiming for a voltage drop no larger than 2.5% of the system voltage. Higher drops waste energy as heat, increase current draw, can cause inverters to trigger low‑voltage alarms, and may lead to undercharged batteries. The guide also points out that resistance comes not just from the cable itself but from fuses, shunts, circuit breakers, terminals and every connection. Keeping cables short, using adequate thickness, making clean tight connections, and choosing a higher system voltage all help minimize voltage drop. For practical wiring advice, visit Cables and Connectors and Electrical Safety.

7. Production estimates come from PVWatts, not a formula

Unlike the electrical calculations above, the energy a solar panel will produce over a year cannot be reduced to a simple formula. It depends on the amount of sunlight at your location, the panel’s orientation and tilt, shading, temperature, and other variables. The National Laboratory of the Rockies (formerly NREL) offers the PVWatts calculator to handle this complexity. PVWatts estimates the energy production of grid‑connected photovoltaic systems. Its inputs include location, system size, module type, array type, tilt, azimuth and system losses, and the tool’s page says its expected range is based on 30 years of actual weather data at the location. The page also cautions that predictions include many inherent assumptions and uncertainties, and do not reflect differences between modules or site‑specific characteristics except as represented by its inputs. For a fixed array, a modeled estimate from a tool like PVWatts is a better starting point than a single multiplier. Learn more in Solar Calculators and Energy Production.

Worksheet: solar sizing formulas at a glance

Use the table below to record your own numbers. The examples come from the sources cited in this article.

Frequently asked questions

How do I estimate daily energy use for a device that cycles on and off?

The Virginia Cooperative Extension recommends that for a refrigerator, you divide the total time it is plugged in by three to approximate the hours the compressor actually runs. For other cycling appliances, you can use a clamp‑on ammeter to measure the running current, multiply by the voltage to get watts, and then estimate the duty cycle based on observation or the appliance’s specifications.

Why does a higher system voltage reduce voltage drop?

Victron’s Wiring Unlimited guide shows that for a fixed power load, doubling the voltage halves the current. Since voltage drop equals current times resistance, a lower current produces a smaller voltage drop across the same cable. Victron’s guide also advises considering a higher system voltage first to avoid very thick cables in systems with a large inverter.

Can I calculate solar panel output with a simple formula?

Not reliably. Output depends on the sunlight at your location, which varies with time of day, season and weather, and on how the array is installed. PVWatts models these inputs for a specific location, and its page still describes the results as estimates with inherent assumptions and uncertainties.

For more tools to help you plan your system, visit our Solar Tools and Calculators page, which collects calculator guides, planning worksheets and measurement tool guides.

Sources

• Virginia Cooperative Extension: Estimating Appliance and Home Electronic Energy Use
• U.S. Energy Information Administration: Measuring electricity
• Victron Energy: Wiring Unlimited
• National Laboratory of the Rockies: PVWatts Calculator