Power Calculator

The power calculator computes the rate at which work is done or energy is transferred, and solves for any one of the variables in four standard power formulas. It is used by mechanical and electrical engineers sizing motors and generators, by automotive engineers rating engine output, by athletes and coaches measuring sustained performance, by renewable-energy designers sizing solar arrays and wind turbines, by HVAC technicians sizing heating and cooling equipment, by electricians sizing circuits and breakers, and by students learning the rate-versus-total distinction that separates power from energy. Power is energy per unit time; high power means doing the same work in less time, or doing more work in the same time.

How to Use the Power Calculator

1. Pick the Mode that matches your problem: Work/Time, Force × Velocity, DC Electrical, or AC Electrical.
2. Pick the variable to Solve for in the second dropdown. The remaining fields become inputs.
3. Enter the input values in SI units (W, J, s, N, m/s, V, A). For AC, also enter the power factor cos(φ) between 0 and 1.
4. The result panel updates instantly and shows the formula used plus practical equivalents (kW, hp, kJ/h for power results; Wh, kWh, cal for work results).

All four modes use closed-form arithmetic: each result is exact up to floating-point precision, with no iterative solvers, no random sampling, and no machine-learning model that might drift between versions.

Formulas

The calculator implements four formulas that all express the same underlying definition, power is energy per unit time, specialised to a particular physical setting.

Mechanical: Work divided by time

P = W / t

The textbook definition. Use it when you know how much work (or energy) is being transferred and over what interval. Rearranged:

• W = P × t, energy delivered by a known power over a known time.
• t = W / P, time required to deliver a known energy at a known power.

For instantaneous power where the rate varies with time, the limit form is P = dW/dt, which generalises the average-power formula above.

Mechanical: Force times velocity

P = F × v

When an object is pushed (or pulled) by a constant force F while moving at velocity v, the power delivered equals their product. This is the form most relevant for transport, overcoming aerodynamic drag and rolling resistance at a steady cruise consumes roughly P_drag = F_drag × v watts.

Rearranged:

• F = P / v, force corresponding to a known power at a known velocity.
• v = P / F, velocity produced by a known power against a known opposing force.

For rotating machinery the analogous form is P = τ × ω, where τ is torque (N·m) and ω is angular velocity (rad/s). Engine dynamometer output is computed this way from torque and RPM.

DC electrical: Voltage times current

P = V × I

For a resistive DC load (or any purely resistive element in DC steady state), the power dissipated equals the product of voltage across the element and current through it. The two equivalent forms P = I² R = V² / R come from combining P = V × I with Ohm's law V = I R.

Rearranged:

• V = P / I, supply voltage required to deliver power P at current I.
• I = P / V, current drawn by a load of power P at voltage V.

These are the formulas used to rate solar panels (W = V × I at the maximum-power point), DC motors, battery chargers, and any DC circuit where knowing voltage and current is enough to compute power.

AC electrical: Voltage, current, and power factor

P = V × I × cos(φ)

For single-phase AC, the real (or true) power delivered to a load is the product of RMS voltage, RMS current, and the power factor cos(φ). The power factor accounts for the phase angle φ between voltage and current waveforms; it equals 1 for purely resistive loads, 0 for purely reactive loads, and is between 0 and 1 for everything in between (motors, transformers, fluorescent ballasts, switch-mode power supplies).

Rearranged:

• V = P / (I × cos(φ))
• I = P / (V × cos(φ))
• cos(φ) = P / (V × I), measured power factor for an AC load given voltmeter, ammeter, and wattmeter readings.

For balanced three-phase AC, the formula becomes P = √3 × V_L × I_L × cos(φ) where V_L and I_L are the line-to-line RMS voltage and line RMS current. That variant is not covered here; this calculator is single-phase only.

Worked Examples

Example 1, Lifting a weight.

A 1,000 J task (lifting a heavy box to a shelf) is done in 5 seconds. Power = W / t = 1,000 / 5 = 200 W. The same task done in 2 seconds would require 500 W, five times the muscular power output.

Example 2, Vehicle at constant speed.

A car cruising at 27 m/s (about 97 km/h) experiences a combined drag and rolling-resistance force of 700 N. Power needed to maintain speed: P = F × v = 700 × 27 = 18,900 W ≈ 19 kW (about 25 hp). Real engines need 2-3× more power because internal-combustion engines are only 30-40% efficient at converting fuel heat to mechanical output.

Example 3, DC circuit.

A 12 V battery powers a device drawing 2 A. Power = V × I = 12 × 2 = 24 W. Over one hour that delivers 24 Wh = 86.4 kJ of energy. If the device is resistive (say, a heating element), the resistance is R = V / I = 6 Ω, and the same result comes from P = V² / R = 144 / 6 = 24 W.

Example 4, AC motor.

A 120 V AC motor draws 0.5 A and operates at a power factor of 0.8 (typical for an induction motor under load). Real power = V × I × cos(φ) = 120 × 0.5 × 0.8 = 48 W. The apparent power (what the utility meters in VA) is V × I = 60 VA; the difference of 12 VAR is reactive power circulating in the motor's inductance.

Example 5, Solar panel.

A 400 W solar panel under standard test conditions delivers 400 W of DC electrical power at its maximum-power point. Over a 5-hour sunny window: W = P × t = 400 × 5 × 3,600 = 7.2 MJ ≈ 2 kWh. That is enough to power an efficient refrigerator for a day, or charge an electric vehicle for a short commute.

Where It Shows Up

• Electric motors and generators. Nameplate power ratings in watts or kilowatts. Motor efficiency curves compare mechanical output power to electrical input power.
• Internal-combustion engines. Peak power in kW or hp; torque × RPM (the rotational P = τω) curves; continuous versus peak ratings.
• Battery and charger sizing. Battery capacity is energy (Wh, kWh); charger and discharge rates are power (W). A 100 Wh battery discharged at 20 W lasts 5 hours; the same battery discharged at 100 W lasts 1 hour.
• Solar and wind generation. Panel peak power (W) and inverter AC output rating; daily energy yield = average power × sunlight hours.
• Electrical grid and household wiring. Circuit breakers rated in amps at a fixed voltage correspond to a maximum continuous power (e.g. 16 A × 230 V ≈ 3.7 kW in European residential wiring).
• Human physiology and athletic performance. Sustained human power output is roughly 75-100 W at rest, 200-400 W for trained cyclists over an hour, and can briefly exceed 2 kW during a sprint or jump.
• Heating, ventilation, and air conditioning (HVAC). Furnace and air-conditioner capacity in watts (or BTU/h, where 1 W ≈ 3.412 BTU/h) tells you how fast the equipment moves heat.

Common Mistakes

Confusing power and energy. Power is a rate (W, kW); energy is a quantity (J, kWh). A 1 kW heater running for 1 hour uses 1 kWh of energy. A 10 kW heater running for 1 hour uses 10 kWh. They are not interchangeable. Battery capacity is energy; motor rating is power.

Mixing up RMS and peak for AC. The formulas above use RMS (root-mean-square) voltage and current, which are what AC voltmeters and ammeters display. The peak values are larger by a factor of √2 for a sine wave. Mixing RMS and peak in P = V × I × cos(φ) silently inflates the result by 2×.

Forgetting the power factor on AC. A reading of 120 V × 5 A on an AC outlet does not mean the load is drawing 600 W. If the power factor is 0.5, the load is drawing 300 W of real power and circulating 300 VAR of reactive power through the wiring. Power factor must be measured (or estimated from the load type) to get the real number.

Using P = V × I for non-resistive DC. Strictly, P = V × I gives the power delivered to any two-terminal element regardless of what it is. For a battery being charged, V and I are still the right inputs, but the sign convention matters: charging power is conventionally negative when you write V and I as the battery's terminal voltage and current, and positive when written from the charger's perspective. Use a consistent sign convention when an answer should be a debit or credit.

Rounding intermediate values. When chaining calculations (e.g. force × velocity, where the force itself came from a drag equation), round only at the end. Premature rounding accumulates across steps and shifts the final answer by a few percent, enough to matter when sizing components or checking an energy budget.

Confusing average and peak power. Engines, motors, solar panels, and even humans have a peak power (briefly achievable) and a continuous rating (sustainable). Circuit breakers, wire gauges, and heat sinks should be sized from the continuous rating, not the peak.

Frequently Asked Questions

What is power? Power is the rate at which work is done or energy is transferred: P = dW/dt. The SI unit is the watt (W), equal to one joule per second. Power measures how fast energy moves, not how much total energy is involved.

What is the difference between power and energy? Power is a rate (energy per unit time); energy is the total quantity moved. A 100 W light bulb and a 1,500 W kettle can both consume the same total energy, the bulb just takes 15× longer. Battery capacity is measured in energy units (Wh, kWh); charger ratings are in power units (W).

Who invented the watt? James Watt (1736-1819) introduced the horsepower unit in the late 18th century to compare steam engines to draft horses. The watt, named in his honour, was adopted as the SI unit of power at the 11th General Conference on Weights and Measures in 1960.

What is horsepower? Mechanical horsepower (hp or bhp) is 745.7 W. Metric horsepower (PS or CV) is 735.5 W. Boiler horsepower is approximately 9,810 W. Watt's original definition came from observing a horse turning a mill wheel, roughly 33,000 foot-pounds per minute of mechanical work.

What is the AC power factor? The power factor cos(φ) is the cosine of the phase angle between AC voltage and current. It equals 1 for purely resistive loads (incandescent bulbs, electric heaters), and is lower for inductive loads (motors, transformers) and capacitive loads. Real AC power is P = V × I × cos(φ), while apparent power is V × I in volt-amperes (VA).

How do I convert watts to horsepower? Divide by 745.7 for mechanical horsepower, or by 735.5 for metric horsepower. A 100 W device is about 0.134 hp. A 1 hp motor is 745.7 W.

How do I convert watts to BTU per hour? Multiply by 3.412. A 1,000 W heater delivers about 3,412 BTU/h, useful when sizing HVAC equipment or comparing with US appliance ratings.

Why are there different power formulas for DC and AC? In DC the voltage and current are constant, so the average and instantaneous power are the same and the formula is simply P = V × I. In AC the voltage and current oscillate, and the time-averaged real power depends on the phase angle between them, giving P = V × I × cos(φ). Reactive loads store and release energy each cycle without dissipating it, which is why the power factor matters.

can the Power Calculator be used for professional or commercial purposes? yes, the Power Calculator The Power Calculator provides mathematically correct results that are suitable for professional, commercial, and educational use. the Power Calculator formulas used are well-established and validated against reference standards.

**How often are the formulas behind the Power Calculator updated? When standards change (e.g., new physical constants, revised SI realisations), this calculator is updated to reflect the current authoritative source. Each calculator's references section, including the Power Calculator, lists the specific sources used.

References

• BIPM. The International System of Units (SI), 9th edition. Bureau International des Poids et Mesures.
• IEEE. IEEE Std 100: The Authoritative Dictionary of IEEE Standards Terms. Institute of Electrical and Electronics Engineers.
• Halliday, D., Resnick, R., & Walker, J. Fundamentals of Physics. Wiley.
• Serway, R. A. & Jewett, J. W. Physics for Scientists and Engineers. Cengage.
• NIST. Reference Constants, Units, and Uncertainty. https://physics.nist.gov/cuu/Constants/
• IUPAP. Symbols, Units, Nomenclature and Fundamental Constants in Physics (the "SUNAMCO" Red Book).