Ohms to Kilowatts Converter
A 230 volt supply across a 50 ohm heating element delivers about 1.06 kilowatts.
Quick answer: Square the voltage, divide by the resistance, then divide by 1,000. For example, 230 V across 50 ohms is 1.058 kW, 120 V across 24 ohms is 0.6 kW and 12 V across 3 ohms is 0.048 kW.
The ohms to kilowatts formula
Power in kilowatts equals voltage squared divided by resistance, divided by 1,000.
Ohms alone cannot give power. You also need the voltage across the part.
Take 230 V across 50 ohms. 230² ÷ 50 ÷ 1,000 gives 1.058 kW.
Take 120 V across 24 ohms. 120² ÷ 24 ÷ 1,000 gives 0.6 kW.
Power from voltage and resistance
For a resistor, the power equals the voltage squared divided by the resistance, and it is measured in watts (Georgia Tech: Power in a circuit).
Dividing by 1,000 changes watts into kilowatts.
How to convert ohms to kilowatts step by step
- Read the voltage across the part and its resistance in ohms.
- Multiply the voltage by itself.
- Divide the result by the resistance to get watts.
- Divide by 1,000 to get kilowatts.
Example 1: 230 V across 50 ohms
- Start with 230 V across 50 ohms.
- 230² ÷ 50 ÷ 1,000 = 1.058.
- The power is 1.058 kW.
230 V across 50 ohms = 1.058 kW
Example 2: 120 V across 24 ohms
- Start with 120 V across 24 ohms.
- 120² ÷ 24 ÷ 1,000 = 0.6.
- The power is 0.6 kW.
120 V across 24 ohms = 0.6 kW
Example 3: 12 V across 3 ohms
- Start with 12 V across 3 ohms.
- 12² ÷ 3 ÷ 1,000 = 0.048.
- The power is 0.048 kW.
12 V across 3 ohms = 0.048 kW
The three examples below use common sizes.
Each one shows the sum in full.
ohms to kilowatts conversion table
| Voltage and resistance | Power (kW) | Power (W) |
|---|---|---|
| 12 V across 3 ohms | 0.048 kW | 48 W |
| 12 V across 6 ohms | 0.024 kW | 24 W |
| 24 V across 12 ohms | 0.048 kW | 48 W |
| 48 V across 24 ohms | 0.096 kW | 96 W |
| 120 V across 24 ohms | 0.6 kW | 600 W |
| 120 V across 10 ohms | 1.44 kW | 1,440 W |
| 230 V across 50 ohms | 1.058 kW | 1,058 W |
| 230 V across 25 ohms | 2.116 kW | 2,116 W |
| 230 V across 100 ohms | 0.529 kW | 529 W |
| 240 V across 57.6 ohms | 1 kW | 1,000 W |
| 400 V across 100 ohms | 1.6 kW | 1,600 W |
| 480 V across 100 ohms | 2.304 kW | 2,304 W |
The highlighted row is the default of the calculator. The last column gives W.
A quick mental shortcut for ohms to kilowatts
Square the volts, divide by the ohms, then move the point three places left. 120 V across 24 ohms is 14,400 / 24 = 600 W, or 0.6 kW.
Double the voltage and the power rises four times.
Cold and hot resistance
The resistance of a heating element or a bulb changes as it warms up. A reading taken cold may not match the resistance when the part is working.
So the result is best for a part at its working temperature.
Power factor and AC loads
For a plain resistor on AC, use the RMS voltage and the formula holds. Loads with coils or capacitors also have reactance, and the real power then depends on the power factor.
This page covers the simple resistive case.
Safety when you measure
Measure resistance with the power off and the part unplugged. Mains voltage can cause serious injury.
If you are not trained to work on mains wiring, ask a qualified electrician.
Quick conversion answers
| Conversion | Result |
|---|---|
| 230 V across 50 ohms | 1.058 kW |
| 120 V across 24 ohms | 0.6 kW |
| 240 V across 57.6 ohms | 1 kW |
| 400 V across 100 ohms | 1.6 kW |
Where this conversion is used
Homeowners estimate the output of a heating element from its resistance and the supply voltage.
Students practise power formulas for resistors.
Common mistakes to avoid
- Using ohms with no voltage. Power needs both numbers.
- Forgetting to square the voltage. Power rises with the square of the voltage.
- Mixing W and kW. One kilowatt is 1,000 watts.
- Using peak voltage on AC. Use the RMS value, such as 230 V.
Related converters
More voltage and resistance pairs
5 V across 10 ohms is 0.0025 kW. 9 V across 18 ohms is 0.0045 kW. 12 V across 0.5 ohms is 0.288 kW.
24 V across 6 ohms is 0.096 kW. 110 V across 30 ohms is 0.4033 kW. 120 V across 14.4 ohms is 1 kW.
220 V across 48.4 ohms is 1 kW. 230 V across 10 ohms is 5.29 kW. 400 V across 50 ohms is 3.2 kW.
Doubling the first number
10 V across 10 ohms is 0.01 kW. 18 V across 18 ohms is 0.018 kW. 24 V across 0.5 ohms is 1.152 kW.
48 V across 6 ohms is 0.384 kW. 220 V across 30 ohms is 1.613 kW. 240 V across 14.4 ohms is 4 kW.
440 V across 48.4 ohms is 4 kW. 460 V across 10 ohms is 21.16 kW. 800 V across 50 ohms is 12.8 kW.
The same element at different supply voltages
110 V across 50 ohms is 0.242 kW. 120 V across 50 ohms is 0.288 kW. 230 V across 50 ohms is 1.058 kW.
240 V across 50 ohms is 1.152 kW.
Frequently asked questions
How do I convert ohms to kilowatts?
You cannot do it from ohms alone. Square the voltage, divide by the ohms, then divide by 1,000.
How many kW is 230 V across 50 ohms?
About 1.058 kW, which is 1,058 W.
Why do I need the voltage?
Power depends on both the voltage and the resistance.
What happens if I double the voltage?
The power rises four times, because the voltage is squared.
Does this work on AC?
Yes for a plain resistor, if you use the RMS voltage.
Is it safe to measure a live heater?
No. Measure resistance with the power off and the part unplugged.
Sources
- Georgia Tech: Power in a circuit (physicsbook.gatech.edu)
