Ohm's law says current equals voltage divided by resistance: I = V ÷ R. Add the power law, P = V × I, and any two of volts, amps, ohms and watts give you the other two. A 1,500 watt space heater on a 120 volt outlet draws 12.5 amps and has a hot resistance of 9.6 ohms, which is why it takes most of a 15 amp circuit on its own.
How the Ohm's law calculator works
HyperPhysics (Georgia State University) states the two relationships the tool combines: the current through a conductor is proportional to the voltage across it, with resistance as the ratio (V = I × R), and electric power is voltage times current (P = V × I). Substituting one into the other gives the twelve formulas on the wheel, three for each quantity:
V = I × R; I = V ÷ R; R = V ÷ I; P = V × I = I² × R = V² ÷ R
Pick the pair you know, type the two values, and the calculator solves the other two. The wheel marks your two known quantities and lights up the formula it used for each unknown, and the math panel prints both with your numbers.
Worked example: a 1,500 W heater at 120 V
With volts and watts known:
- Current: I = P ÷ V = 1,500 W ÷ 120 V = 12.5 A
- Resistance: R = V² ÷ P = (120 V)² ÷ 1,500 W = 14,400 ÷ 1,500 = 9.6 Ω
Check it with the other formulas: 12.5 A × 9.6 Ω = 120 V, and (12.5 A)² × 9.6 Ω = 1,500 W.
Now put the same heating element on 240 V. Resistance stays 9.6 Ω, so current doubles to 25 A and power quadruples to 6,000 W (P = V² ÷ R). That is why a 120 V appliance must never be connected to 240 V. The reverse is also true: a heater built for 3,000 W at 240 V has 19.2 Ω and puts out only 750 W at 120 V.
Formulas for each quantity
| Find | From volts and amps | From amps and ohms | From volts and ohms | With watts |
|---|---|---|---|---|
| Volts (V) | known | I × R | known | P ÷ I, √(P × R) |
| Amps (I) | known | known | V ÷ R | P ÷ V, √(P ÷ R) |
| Ohms (R) | V ÷ I | known | known | V² ÷ P, P ÷ I² |
| Watts (P) | V × I | I² × R | V² ÷ R | known |
Resistors in series and in parallel
Switch the tool to Series or Parallel to combine resistors. HyperPhysics derives both rules from Ohm's law and the circuit laws:
- Series: resistances add. 100 Ω + 220 Ω + 330 Ω = 650 Ω. On 12 V the string draws 12 ÷ 650 = 18.5 mA and dissipates 0.22 W.
- Parallel: reciprocals add. 1 ÷ (1/100 + 1/220 + 1/330) = 56.9 Ω, less than the smallest resistor. On 12 V it draws 0.211 A and 2.53 W.
Two equal resistors in parallel always halve: two 100 Ω resistors make 50 Ω. Enter a supply voltage to see the current and power of the whole network.
Where Ohm's law stops
Ohm's law is exact for resistive loads such as heaters, toasters, incandescent bulbs and resistors. A motor, compressor or LED driver has a power factor below 1, so volts times amps overstates the real watts. For those loads, use the amp calculator, which adds power factor, efficiency and three-phase circuits.
Resistance also changes with temperature. A tungsten filament measured cold with a meter reads far lower than its hot resistance, and copper wire gains about 0.3% resistance per °C, which Chapter 9 Table 8 of the NEC accounts for by listing wire resistance at 75 °C.
Using the answer on a real circuit
The current you get is the number that sizes everything downstream. Match it to a breaker with the breaker size calculator, choose the conductor with the wire size calculator, and on long runs check the voltage drop, which is Ohm's law applied to the wire itself: current times the wire's resistance. Every related tool is on the electrical calculators page.