The relationship between voltage, current, and resistance
Electrical circuits obey predictable rules. Ohm's Law expresses the core relationship: increase the voltage pushing electrons through a circuit, and more current flows; increase the resistance blocking that flow, and current drops. Power—the rate at which energy is used—ties all three together.
How it works
This calculator uses the fundamental equations of electrical circuits to find any missing value when you provide two knowns:
- V = I × R (voltage equals current times resistance)
- P = V × I (power equals voltage times current)
- P = I² × R (power equals current squared times resistance)
- P = V² / R (power equals voltage squared divided by resistance)
You can input any pair: voltage and current, voltage and resistance, current and resistance, power and voltage, or power and current. The calculator solves the system of equations to return all four values.
The formula
V = I × R and P = V × I
Worked example
Suppose you have a household light bulb rated at 60 watts running on 120 volts (typical in North America). What is the resistance and current?
Given:
- Power (P) = 60 W
- Voltage (V) = 120 V
Step 1: Find current using P = V × I
60 = 120 × I
I = 60 ÷ 120 = 0.5 A
Step 2: Find resistance using V = I × R
120 = 0.5 × R
R = 120 ÷ 0.5 = 240 Ω
Results:
- Current: 0.5 amperes
- Resistance: 240 ohms
- Voltage: 120 volts (confirmed)
- Power: 60 watts (confirmed)
This tells you the bulb draws half an amp of current and has an internal resistance of 240 ohms. If you wanted a dimmer bulb using the same 120 V supply, you'd need one with higher resistance, which would draw less current and use less power.
Common mistakes to avoid
Unit confusion: Mixing units (e.g., milliamps with amps, kilohms with ohms) is the most common error. Always convert to base units (volts, amperes, ohms, watts) before entering values.
Forgetting power relationships: Power is not independent—it's always determined by V, I, and R. If you calculate current and resistance correctly, power will follow automatically. Don't try to enter a power value that contradicts your other inputs.
Assuming constant resistance: In real circuits, resistance can change with temperature. A cold filament has lower resistance than a hot one, so current surges briefly when you switch on an incandescent bulb. Ohm's Law applies at any instant, but resistance isn't always truly constant.
Zero or negative values: Negative voltage, current, or resistance have no meaning in standard DC circuits. Zero resistance creates a short circuit (infinite current), and zero current means no power flow. The calculator requires positive, non-zero inputs.
This calculator is an estimate based on Ohm's Law and power relationships. Real circuits may behave differently due to non-linear elements, temperature effects, or AC frequency. For critical engineering or safety-sensitive applications, consult a qualified electrician or engineer.