Joule Heating Calculator
Solve the Joule heating law P = I²R = V²/R = VI for any unknown, convert heating energy over time, and estimate temperature rise. Everything runs in your browser.
Which tool for which question?
• This tool = electric heating: heater elements, wire heating, the I²R law, heating energy, temperature rise.
• wattage-calculator = appliance wattage, PC power-supply sizing, power factor, electricity bills.
• newton-to-joules = mechanical work E = F·d (force moving an object), not electric heating.
• kw-to-joules / volts-to-joules-calculator = unit conversion of energy, or battery/capacitor energy (V·Q, ½CV²).
• This tool = electric heating: heater elements, wire heating, the I²R law, heating energy, temperature rise.
• wattage-calculator = appliance wattage, PC power-supply sizing, power factor, electricity bills.
• newton-to-joules = mechanical work E = F·d (force moving an object), not electric heating.
• kw-to-joules / volts-to-joules-calculator = unit conversion of energy, or battery/capacitor energy (V·Q, ½CV²).
Joule heating solver (P, I, V, R)
Fill in at least two values (magnitudes only; heating depends on I²). The solver derives the rest and cross-checks all three power formulas.
Heating energy & time
Temperature rise estimate
Idealized: ΔT = E / (m·c). Assumes no heat loss and uniform temperature, so the real rise is lower.
Disclaimer: this is an idealized upper bound. Real objects lose heat to the air, contacts, and radiation, and temperature is never perfectly uniform. Do not use this for safety-critical thermal design.
Formula reference
| Solve for | Given | Formula |
|---|---|---|
| Power P | I, R | P = I²R |
| Power P | V, R | P = V²/R |
| Power P | V, I | P = VI |
| Current I | P, R | I = √(P/R) |
| Current I | V, R | I = V/R |
| Voltage V | I, R | V = IR |
| Voltage V | P, R | V = √(PR) |
| Resistance R | V, I | R = V/I |
| Resistance R | P, I | R = P/I² |
| Energy E | P, t | E = P·t |
| Temp. rise ΔT | E, m, c | ΔT = E/(m·c) |
Frequently asked questions
What is Joule heating?
Joule heating is the process by which an electric current passing through a conductor releases heat. The heating power is P = I squared times R, where I is the current in amperes and R is the resistance in ohms. It is the reason heater elements, incandescent filaments, fuses, and overloaded wires get hot.
How do I calculate Joule heating power?
Enter any two of power, current, voltage, and resistance, and the calculator solves the rest. Example: a current of 2 A through a 10 ohm resistor gives P = I squared times R = 2 squared times 10 = 40 W. The voltage across the resistor is V = I R = 20 V, and all three forms agree: I squared R = 40 W, V squared / R = 400 / 10 = 40 W, and V I = 40 W.
What are the three formulas for electric heating power?
P = I squared R, P = V squared / R, and P = V I. They are the same physical law combined with Ohm's law (V = I R), so a consistent set of inputs always gives the same power from all three. Use I squared R when the current is fixed (series circuits, fuses), V squared / R when the voltage is fixed (mains-powered heaters), and V I when you measure voltage and current directly.
How much energy does a 40 W heater use in 30 minutes?
Energy is E = P times t. 40 W for 30 minutes (1800 s) gives E = 40 times 1800 = 72000 J. That equals 20 Wh, 0.02 kWh, about 17208.4 calories, or about 68.2428 BTU.
How do I estimate the temperature rise?
For an idealized estimate with no heat loss, delta-T = E / (m times c), where m is the mass in kg and c is the specific heat in J/kg K. Example: 72000 J absorbed by 0.5 kg of water (c = 4184 J/kg K) raises its temperature by about 34.4168 K, which is the same as 34.4168 degrees C. Real heating is always lower because heat escapes to the surroundings; treat this as an upper bound.
Worked example: 100 W across a 5 ohm heater?
Current I = square root of (P / R) = square root of 20 = about 4.47214 A. Voltage V = I R = about 22.3607 V. Check: V squared / R = 500 / 5 = 100 W, consistent.
Why does the calculator reject negative values?
Joule heating depends on I squared, so only the magnitude of the current matters, and the resistance of a passive heater cannot be negative. Enter positive magnitudes; the tool reports an error otherwise instead of silently producing a misleading result.
Which units are supported?
Power: W, kW, MW. Current: A, mA. Voltage: V, mV, kV. Resistance: ohm, kohm, Mohm. Time: s, min, h, day. Energy results: J, kJ, Wh, kWh, cal, kcal, BTU. Mass: kg, g.
How is this different from mechanical work in joules?
Same joule, different physics. The newton-to-joules calculator computes mechanical work E = F times d, a force moving an object. This tool computes electrical heating from P = I squared R: current through resistance. Use newton-to-joules for forces and distances; use this tool for heater elements and wire heating.
How is this different from the wattage calculator?
The wattage-calculator sizes appliance wattage, PC power supplies, power factor, and electricity bills. This tool is about resistive heating itself: the I squared R law, heater-element and wire-heating problems, heating energy over time, and temperature-rise estimates.
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