Ohm's law calculator

What V, I and R actually are

Think of a water pipe. Voltage (V) is the pressure pushing water into the pipe. Current (I) is how many litres per second actually flow. Resistance (R) is how narrow the pipe is — a thin pipe fights the push, a fat pipe lets water through easily. Ohm's law says these three are locked together: push harder (more V) and more flows (more I); use a narrower pipe (more R) and less flows (less I). In an equation: V = I × R.

Rearranging it

You almost never have all three — you have two and want the third. Divide both sides of V = I × R to flip the equation three ways:

• I = V ÷ R — "with this battery and this resistor, how much current flows?"
• R = V ÷ I — "I want 10 mA from a 4.5 V battery — which resistor?"
• V = I × R — "20 mA through a 220 Ω resistor needs how big a battery?"

The calculator picks the right one for you. The numbers it prints are the exact numbers the engine runs below — a pure resistor-and-battery loop has no diode curve to confuse things, so Ohm's law holds dead-on.

And one more — power

Current flowing through resistance makes heat. That's power, measured in watts: P = V × I. A normal ¼-watt (250 mW) resistor handles everything on a hobby bench; the only time you'll see heat matter is at very low resistance across a bigger battery — try "find current" with 4.5 V and 10 Ω and watch the mW number climb.

Common questions

Why milliamps instead of amps? Hobby circuits run on tiny currents. An LED is comfortable at 10–20 mA (0.010–0.020 A); a buzzer draws about 15 mA. Writing "0.020 A" everywhere is clumsy, so everyone uses milliamps — 20 mA — instead. The calculator uses mA for input and output; the math inside converts to amps.

What if I pick a resistance that doesn't exist? Resistors come in a fixed set of values (the E12 series: 100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820 and their multiples). "Find R" rounds the answer and shows the nearest real part, so you know what to actually grab. The resistor color code calculator turns that number into the paint bands on the body.

What about LEDs? An LED is not a resistor — its forward voltage behaves differently, and Ohm's law alone will cook it. For LEDs, use the LED resistor calculator instead; it does the "voltage left for the resistor" step first, then applies Ohm's law to that remainder.

Build the physical loop in First Light, or read the longer story on the Ohm's law skill page.