ElectroHub

Joule Heating Calculator

Every ampere pushed through a resistance turns electrical energy into heat. Joule's law says how much — the basis of heaters, fuses, and every thermal failure you have ever debugged.

Joule's Heating — H = I²Rt

Heat energy produced by a current in a resistance. Add the mass and specific heat of the heated body to also get its temperature rise (water c = 4184 J/kg·°C).

Heat produced
In calories
In units (kWh)
Heating power
  1. 1.Given: I = 5 A, R = 10 Ω, t = 300 s
  2. 2.FormulaHeat H = I²·R·tSubstituteH = 5² × 10 × 300ResultH = 75 kJ
  3. 3.FormulaIn calories: H ÷ 4.184Substitute= 75000 ÷ 4.184Result= 17925.4302 cal
Common trap: Heat depends on the squareof current — double the current and you get four times the heat for the same resistor. That's why fuses and cable ratings care about current, and why high-voltage/low-current transmission wastes far less as heat.

The formula

H = I² × R × t

H
heat energy produced (joules)
I
current (amperes)
R
resistance (ohms)
t
time the current flows (seconds)

Worked example

2 A through a 10 Ω element for 60 seconds.

  1. H = I² × R × t
  2. H = 2² × 10 × 60 = 4 × 10 × 60
  3. In calories: 2400 / 4.184 ≈ 574 cal

H = 2400 J (about 574 calories).

Where you'll use it

Heater and fuse design, working out how hot a resistor will actually get, and the classic problem about the time taken to boil a given mass of water.

The laws behind it

Parts this applies to

Resistor (fixed)Varistor / MOVTVS / Transient SuppressorIGBTSCR (Thyristor)Linear Regulator (78xx / LDO)Switches (toggle/push/slide/rotary/DIP)Solid-State Relay (SSR)

Related calculators

Electrical Power CalculatorP = V × I = I² × R = V² / REnergy and Electricity Bill CalculatorUnits (kWh) = (Watts / 1000) × hoursWire Voltage Drop CalculatorR_cable = ρ × (2 × L) / A