Ohm's Law and the Power Triangle — Every Formula You Need

Three formulas power all of basic electronics: V = IR, P = IV, and P = I²R. If you know any two of voltage, current, resistance, and power — you can calculate the other two. The power calculator does exactly this. Enter any two values, get the rest.

The core relationships

Ohm's Law

V = I × R

Voltage (volts) equals current (amps) times resistance (ohms).

Rearranged:

• I = V / R — current through a component
• R = V / I — effective resistance

Power formula

P = I × V

Power (watts) equals current (amps) times voltage (volts).

Combined with Ohm's Law:

• P = I² × R — power from current and resistance
• P = V² / R — power from voltage and resistance

The 12 formulas

Every electronics reference shows the "Ohm's Law wheel" with 12 formula variations. They're all derived from V = IR and P = IV:

Find	Using V and I	Using V and R	Using I and R	Using P and...
V	V = V	V = V	V = I×R	V = P/I or √(P×R)
I	I = I	I = V/R	I = I	I = P/V or √(P/R)
R	R = V/I	R = R	R = R	R = V²/P or P/I²
P	P = V×I	P = V²/R	P = I²×R	P = P

You don't need to memorize all 12. Know V = IR and P = IV, and derive the rest.

Worked examples

USB power delivery

A USB port supplies 5V. Your device draws 500 mA (0.5 A).

• Power: P = 5 × 0.5 = 2.5 W
• If the USB cable has 0.5 Ω resistance: voltage drop = 0.5 × 0.5 = 0.25 V (device sees 4.75V)
• Power lost in the cable: P = 0.5² × 0.5 = 0.125 W

This is why cheap USB cables cause charging problems — high cable resistance drops the voltage below what the device needs.

Heating element

A 1000W kettle on 230V mains:

• Current: I = P/V = 1000/230 = 4.35 A
• Resistance: R = V²/P = 230²/1000 = 52.9 Ω
• Or: R = V/I = 230/4.35 = 52.9 Ω (same answer, different path)

LED current limiting

A red LED (1.8V forward voltage) on a 5V supply with a 220 Ω resistor:

• Voltage across resistor: 5 − 1.8 = 3.2V
• Current: I = 3.2/220 = 14.5 mA
• Power in resistor: P = 3.2 × 0.0145 = 0.046 W (46 mW — well within a ¼W resistor's rating)

Choosing a fuse

Your 12V circuit should draw no more than 2A.

• Expected power: P = 12 × 2 = 24 W
• Use a 2.5A or 3A fuse — enough headroom for startup surges but will blow before damaging wiring

Power dissipation and heat

Every resistor converts electrical energy to heat. This matters:

Resistor rating	Max power	Typical size
1/8 W (0.125W)	Small signal	1.6mm axial
1/4 W (0.25W)	Most common	2.3mm axial
1/2 W (0.5W)	Moderate loads	3.5mm axial
1 W	Power circuits	5mm axial
5 W	Heatsink territory	Ceramic block

Rule of thumb: Derate by 50%. If a resistor will dissipate 0.2W, use at least a 1/2W resistor. Running at full rated power shortens lifespan and makes the component too hot to touch.

Use the power calculator to check power dissipation before building. Enter voltage across the resistor and its resistance to see the wattage.

Series and parallel

Series resistors

R_total = R1 + R2 + R3 + ...

Current is the same through all. Voltage divides proportionally. Use series resistors to increase total resistance or create voltage dividers.

Parallel resistors

1/R_total = 1/R1 + 1/R2 + 1/R3 + ...

For two resistors: R_total = (R1 × R2) / (R1 + R2)

Voltage is the same across all. Current divides proportionally. Use parallel resistors to decrease total resistance or share power dissipation.

Example: Two 100 Ω resistors in parallel = 50 Ω, and each dissipates half the power.

When Ohm's Law doesn't apply

Ohm's Law works for linear, passive components — resistors, wire, heating elements. It doesn't directly apply to:

• LEDs and diodes — nonlinear V-I relationship (but Ohm's Law still governs the series resistor)
• Capacitors and inductors — impedance varies with frequency
• Transistors — controlled by gate/base voltage, not simply V/R
• Switched-mode converters — power in ≈ power out, but voltage and current ratios change

For the resistive parts of any circuit, V = IR still applies. It's the foundation you build everything else on.

Quick sanity checks

Before powering a circuit, mentally verify:

1. Total current draw — does it exceed your supply's capacity?
2. Voltage drops — do they add up to the supply voltage in a series loop?
3. Power dissipation — is any component exceeding its rating?

If any of these feel wrong, run the numbers through the Ohm's Law calculator before connecting power. Catching a mistake in software is cheaper than replacing a burned component.

Need to identify resistors for your circuit? The resistor color code decoder converts band colors to values instantly.