Power Calculator
Calculate electrical power from voltage, current, or resistance using the three power equations: P = V × I, P = I² × R, and P = V² / R. Solve for P, V, I, or R.
How to Use
- Pick what to solve for: Power, Voltage, Current, or Resistance.
- Enter any two of the other three values. The tool picks the right formula.
- The power-wheel visualization shows all four equations relating V, I, R, and P.
- Use it to size wire, check heat dissipation, or compute supply current for a load.
Show Work
All 12 Formulas (Power Wheel)
History of the Watt
The watt is named after James Watt (1736–1819), the Scottish engineer whose improvements to the Newcomen steam engine — particularly the separate condenser patented in 1769 — ignited the Industrial Revolution. Watt introduced "horsepower" as a marketing unit to sell steam engines by comparing them to the draft horses they replaced. The International Electrical Congress renamed it at the 1889 Paris exhibition, unifying mechanical, electrical, and thermal power in a single SI unit: one watt equals one joule per second.
The three forms of electrical power (P = V·I, P = I²R, P = V²/R) follow directly from James Prescott Joule's 1841 experiments showing that heat dissipated in a conductor is proportional to the square of the current and to the resistance — "Joule heating." Combined with Ohm's 1827 linear voltage-current law, these produce the "power wheel": twelve algebraic rearrangements of the same three physical facts. Generations of electrical students have memorized it; working engineers just derive the form they need.
Today, wattage ratings on every resistor, transistor, light bulb, and appliance trace back to this chain of 19th-century discoveries. Joule's name lives on as the SI unit of energy; Watt's as the unit of power; Ohm's as the unit of resistance. The calculator on this page is essentially their three equations made interactive.
About This Calculator
Pick what you want to solve for, enter any two of the remaining quantities, and this calculator computes the rest using the correct form of the power equation. The power-wheel visualization highlights which of the twelve formulas is active based on your inputs, so the derivation is never a black box.
The math assumes DC or purely resistive AC (unity power factor). For reactive loads — motors, transformers, capacitor-input supplies — apparent power (VA) diverges from real power (W) and you'll want the AC Power or Three-Phase calculators instead. Everything here runs client-side; no values are transmitted or stored.
Frequently Asked Questions
What's the difference between P = V×I, P = I²R, and P = V²/R?
They're all the same physical quantity, just different inputs. P = V × I is the fundamental definition (work per unit time equals voltage times charge flow). Substituting Ohm's law V = IR gives P = I² × R (power in terms of current), or substituting I = V/R gives P = V² / R (power in terms of voltage). Pick whichever equation uses the two values you know.
When should I care about power?
Any time heat or size matters: resistor wattage ratings, transistor power dissipation, wire gauge selection, heatsink sizing, power supply capacity, battery life, heating elements. For digital logic at low currents you rarely care; for anything above ~100mW you should check.
How much power can a resistor handle?
Look at the wattage rating: common through-hole sizes are 1/8W, 1/4W, 1/2W, 1W, 2W, 5W. Always derate by 2× — a resistor actually dissipating 1/4W in a circuit should be rated at 1/2W minimum. Heat degrades resistors over time; headroom extends lifetime.
Does this work for AC?
Only for purely resistive AC loads using RMS voltage and current. For reactive loads (capacitors, inductors, motors), you need apparent power (VA), real power (W), and power factor (cos φ). This calculator handles the simple DC or resistive-AC case.
What's the difference between power (W) and energy (Wh)?
Power is the instantaneous rate of energy transfer — watts, or joules per second. Energy is power × time: 1 watt sustained for 1 hour = 1 Wh = 3600 J. A 10W LED bulb draws 10W of power; running it for 5h consumes 50Wh of energy.
What does "heat dissipation" mean?
Any power consumed by a resistive element converts to heat. A 100Ω resistor carrying 0.1A dissipates 1W as heat — that's why it feels warm. High-current resistors, MOSFETs, and LDOs need heatsinks because their thermal resistance can't move heat away fast enough to stay below rated junction temperatures.
Common Use Cases
Resistor Wattage Check
You calculated R = 47Ω for a circuit with 100mA — is a 1/4W resistor enough? P = I²R = 0.01 × 47 = 0.47W. No — you need 1W minimum.
Power Supply Sizing
Your board draws 12V at 850mA average. Supply needs to provide 12V × 0.85A = 10.2W continuous, so a 15W adapter is appropriate.
Transistor Power Dissipation
A MOSFET dropping 2V at 5A drain current dissipates 10W as heat. Without a heatsink, that will destroy most TO-220 packages within seconds.
Heating Element Design
Need 100W from a 12V supply for a 3D-printer heat bed. R = V²/P = 144/100 = 1.44Ω. Current will be 100/12 = 8.3A.
Wire Gauge Selection
A wire carrying 15A generates I²R heat. For 20 feet of 14AWG (~0.25Ω/100ft), voltage drop is 15 × 0.05 = 0.75V; power loss = 15 × 0.75 = 11.25W.
Solar Panel / Inverter Sizing
A 400W solar panel feeds a 12V battery system. Max current = 400/12 = 33A. MPPT converter and wiring must handle this peak.
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