Ohm's Law Calculator (V / I / R / P)
Ohm's law is the most basic relationship in a DC circuit: voltage (V) = current (I) × resistance (R). Combined with the electrical power formula P = V × I, knowing any two of the four quantities lets you solve for the other two. This calculator covers all six pairings and auto-formats results with SI prefixes (k, m, µ) so you can read the magnitude at a glance.
Enter valid numbers. Resistance must be > 0 and power must be ≥ 0.
Voltage V
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Derived
Current I
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Derived
Resistance R
—
Derived
Power P
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Derived
Working
V = I × R | P = V × I
DC steady-state: V = IR and P = VI (so P = I²R = V²/R). Results are auto-formatted with SI prefixes (k, m, µ).
Formula
V = I × R // Ohm's law P = V × I // Electrical power P = I² × R // Power from current and resistance P = V² ÷ R // Power from voltage and resistance I = √(P ÷ R) // Current from power and resistance
- · SI units throughout: V = volt, A = ampere, Ω = ohm, W = watt. By definition, 1 V × 1 A = 1 W.
- · Resistance must be > 0 — the calculator rejects R ≤ 0 (an ideal wire would force division by zero in the V/R branch). Passive resistors only dissipate energy, so P ≥ 0 always.
- · Ohm's law applies to "ohmic" components where V/I stays roughly constant: metal-film and carbon-film resistors, copper wire, etc. Semiconductors (diodes, transistors), incandescent filaments, fluorescent lamps and the internal resistance of batteries are non-linear — use their datasheet curves, not a single R value.
- · Valid only for DC steady-state. For AC, replace R with impedance Z (resistance + reactance) and track the phase angle. This calculator does not handle AC.
- · LED current-limiting resistor shortcut: R = (V_supply − V_LED) ÷ I_LED. A red LED with V_F = 2.0 V at 20 mA on a 5 V rail needs R = (5 − 2) ÷ 0.02 = 150 Ω.
- · Results use SI prefixes: 1,500 Ω displays as 1.5 kΩ, 0.025 A as 25 mA, and 0.000001 A as 1 µA.
- · Sources: Hambley, "Electrical Engineering: Principles and Applications"; HKEAA HKDSE Physics Curriculum and Assessment Guide ("Electricity and Magnetism" strand); NIST SI Brochure (definitions of volt, ampere, ohm and watt).
Frequently asked
Does Ohm's law apply to every circuit?
No. Ohm's law V = IR only applies to "ohmic" components — devices where V/I stays roughly constant. That includes metal-film and wirewound resistors and copper wiring. Non-linear devices (diodes, LEDs, transistors, incandescent filaments, transformer loads) have curved V–I characteristics that require a datasheet or a SPICE-style simulator. The calculator also assumes DC steady-state; for AC you must use impedance Z and a phase angle.
How do I size the current-limiting resistor for a 5 V USB-powered LED?
Step 1: look up the LED's forward voltage (V_F) and recommended forward current (I_F). Typical red LEDs: 2.0 V / 20 mA; blue or white LEDs: 3.0 V / 20 mA. Step 2: the resistor drops the remaining voltage: V_R = V_supply − V_F. Step 3: apply Ohm's law: R = (V_supply − V_F) ÷ I_F. For a red LED on 5 V: R = (5 − 2) ÷ 0.02 = 150 Ω. Power dissipated: P = I² × R = 0.02² × 150 = 60 mW, so a standard 1/4 W resistor is fine. In the calculator, pick the "Voltage V & Current I" pair and enter V = 3, I = 0.02.
Why is my electricity bill measured in kWh instead of watts?
Watts measure instantaneous power, but the utility bills you for total energy used, which is power × time. 1 kWh means running a 1000 W appliance for 1 hour. A 1.5 kW air-con running 8 hours a night uses 12 kWh per night, or about 360 kWh per month. Ohm's law itself ignores time, but the wattage P from this calculator multiplied by hours-of-use and the per-kWh tariff (around HK$1.x for CLP / HK Electric) gives the bill in dollars.
Power has three forms — P = VI, P = I²R and P = V²/R. Which one do I use?
All three follow from P = VI plus Ohm's law — they are mathematically identical, so picking one is just about convenience. Use P = VI when V and I are both known; use P = I²R for series circuits where R is fixed (typical resistor heat dissipation problems); use P = V²/R for parallel branches where V is fixed across the resistor. The calculator selects the appropriate identity automatically based on the pair you choose, and shows the formula used below the results.
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