Almost every electrical calculation starts from three quantities and one simple law. Once you know how voltage, current and resistance relate, and how power follows from them, you can size a resistor, check whether a circuit will overheat or estimate what an appliance costs to run. Each example below was computed and can be repeated in the Ohm's Law Calculator.
Voltage, current and resistance
| Quantity | Symbol | Unit | Think of it as |
|---|---|---|---|
| Voltage | V (or U) | volt (V) | The push: the pressure difference that drives charge |
| Current | I | ampere (A) | The flow: how much charge passes per second |
| Resistance | R | ohm (Ω) | The opposition: how hard the path makes it to flow |
| Power | P | watt (W) | The rate at which energy is converted, for example into heat or light |
The water analogy helps: voltage is the pressure in a pipe, current is the flow rate, and resistance is how narrow the pipe is. More pressure or a wider pipe means more flow.
Ohm's law
For a resistor, current is proportional to voltage:
V = I × R, so I = V / R and R = V / I
Example. A 4 Ω heating element on a 12 V supply draws I = 12 / 4 = 3 A.
Doubling the voltage doubles the current; doubling the resistance halves it. The law describes resistors and metal conductors at a steady temperature. Components such as LEDs, diodes and transistors are non-linear: their current is not proportional to voltage, so you apply Ohm's law to the resistor around them instead.
Electrical power
Power is voltage times current, and combining that with Ohm's law gives three equivalent forms:
| Formula | Use it when you know |
|---|---|
| P = V × I | Voltage and current |
| P = I² × R | Current and resistance (heat in a wire or resistor) |
| P = V² / R | Voltage and resistance |
Example, the heating element again. P = 12 × 3 = 36 W, and also 3² × 4 = 36 W and 12² / 4 = 36 W.
Example, a kettle. A 2,000 W kettle on 230 V draws I = 2000 / 230 = 8.70 A and has a resistance of 230² / 2000 = 26.45 Ω. A 1,500 W heater on 120 V draws 12.5 A and has 9.6 Ω. Mains-powered appliances are usually rated in watts, so I = P / V is the formula you will use most to check a circuit's current. The Electrical Power Calculator converts between watts, volts and amps, including three-phase supplies.
Example, heat in a cable. 10 A through a cable with 0.1 Ω of resistance loses 10² × 0.1 = 10 W as heat. Because the loss grows with the square of the current, doubling the current quadruples the heat, which is why thicker cables are needed for bigger loads.
Alternating current
On AC mains, V and I are RMS values (230 V or 120 V are RMS). For resistive loads such as heaters and kettles, P = V × I still holds. Motors and power supplies shift current and voltage out of step, so real power is P = V × I × power factor. A device drawing 5 A at 230 V with a power factor of 0.8 uses 230 × 5 × 0.8 = 920 W of real power, while the supply must carry 1,150 VA of apparent power.
Resistors in series
In series, the same current flows through every resistor, and the resistances add:
R_total = R1 + R2 + R3 + ...
Example. 100 Ω, 220 Ω and 330 Ω in series on 9 V:
| Quantity | Calculation | Result |
|---|---|---|
| Total resistance | 100 + 220 + 330 | 650 Ω |
| Current | 9 / 650 | 13.85 mA |
| Voltage across 100 Ω | 0.013846 × 100 | 1.385 V |
| Voltage across 220 Ω | 0.013846 × 220 | 3.046 V |
| Voltage across 330 Ω | 0.013846 × 330 | 4.569 V |
| Total power | 9 × 0.013846 | 0.125 W |
The voltage drops add back up to the 9 V supply, and the biggest resistor takes the biggest share. Read a resistor's value from its colour bands with the Resistor Calculator.
Resistors in parallel
In parallel, every resistor sees the same voltage, and the currents add. The combined resistance is always smaller than the smallest resistor:
1 / R_total = 1 / R1 + 1 / R2 + ..., and for two resistors R_total = (R1 × R2) / (R1 + R2)
Example. 100 Ω in parallel with 220 Ω: (100 × 220) / 320 = 68.75 Ω. On 9 V the 100 Ω resistor carries 90 mA, the 220 Ω one 40.9 mA, 130.9 mA in total, which is exactly 9 / 68.75.
Shortcuts: two equal resistors in parallel give half the value, three equal ones a third (three 330 Ω give 110 Ω).
Voltage dividers
Two resistors in series split a voltage in proportion to their values:
V_out = V_in × R2 / (R1 + R2)
Example. R1 = 10 kΩ and R2 = 4.7 kΩ on 9 V give V_out = 9 × 4.7 / 14.7 = 2.88 V, with 0.61 mA flowing through both. Two equal resistors give exactly half: 12 V becomes 6 V.
A divider is fine for a reference voltage or for reading a sensor, but not for powering a load: anything connected to the output draws current and pulls the voltage down. Find resistor pairs for a target voltage with the Voltage Divider Calculator.
Worked example: a resistor for an LED
An LED needs its current limited. With a 5 V supply, a red LED with a 2 V forward voltage and a target of 20 mA:
- The resistor must drop the rest: 5 − 2 = 3 V.
- Ohm's law: R = 3 / 0.020 = 150 Ω.
- Power in the resistor: 3 × 0.020 = 0.06 W, so a common 0.25 W resistor has plenty of margin.
If the exact value is not available, pick the next standard value up, which slightly lowers the current. The LED Resistor Calculator does this for several LEDs in series and rounds to E12 or E24 values.
From power to energy and cost
Power is a rate; energy is power multiplied by time, billed in kilowatt-hours:
kWh = watts × hours / 1000
Example. A 60 W lamp on for 5 hours a day for 30 days uses 60 × 5 × 30 / 1000 = 9 kWh. At 0.15 per kWh that costs 1.35 in your currency. A 2,000 W heater running 1.5 hours uses 3 kWh, about the same as that lamp for ten days. Estimate any appliance with the Electricity Calculator.
Common mistakes
- Mixing units. Convert mA to A and kΩ to Ω first: 20 mA is 0.020 A, 4.7 kΩ is 4,700 Ω.
- Ignoring the power rating. A resistor that dissipates more than its rating overheats; choose one rated at least twice the calculated power.
- Adding parallel resistances. Parallel resistances never add up; the result is below the smallest one.
- Using Ohm's law on an LED alone. Apply it to the series resistor, using the voltage left after the LED's forward voltage.
More formulas, including cable voltage drop and battery runtime, are collected in Electrical Formulas Cheat Sheet.