Ohm's Law Calculator

The Ohm's Law wheel combines V = IR with P = VI to create twelve interconnected formulas covering every combination of two known values.

The twelve formulas group by which variable you solve for:

• Voltage: V = IR, V = P/I, V = √(PR)
• Current: I = V/R, I = P/V, I = √(P/R)
• Resistance: R = V/I, R = P/I², R = V²/P
• Power: P = VI, P = I²R, P = V²/R

The last (P = V²/R) is particularly useful for heat-dissipation checks — a 100 Ω resistor across 12 V dissipates 12²/100 = 1.44 W and needs at least a 2 W rating (rule of thumb: pick 2× headroom).

V = IR is most common for series-circuit voltage analysis; I = V/R is standard for finding load current from a known supply. Engineers memorise the wheel within months of working with circuits; until then a printable cheat sheet next to the bench works fine.

Four directions cover everything:

• Find voltage (V = IR): given current and resistance, multiply. 0.5 A × 100 Ω = 50 V.
• Find current (I = V/R): given voltage and resistance, divide. 9 V / 470 Ω ≈ 19.1 mA.
• Find resistance (R = V/I): given voltage and current, divide. 12 V / 0.5 A = 24 Ω.
• Find power (P = VI, or I²R, or V²/R): pick whichever pair you have. 12 V × 2 A = 24 W; equivalently 2² × 6 Ω = 24 W; equivalently 12² / 6 = 24 W.

Always work in SI base units — amperes (not milliamps), ohms (not kilohms), volts (not millivolts) — to avoid factor-of-1000 errors. If your values are in mA or kΩ, convert first or remember the prefix cancellation: 1 mA × 1 kΩ = 1 V (the prefixes cancel cleanly).

Three power formulas all give the same answer; pick the one that matches the values you have.

• P = VI is the most direct: voltage × current. Use when both are known or measurable.
• P = I²R is best for series-circuit power calculations where the same current flows through every component — multiply each resistor by I² to find its individual heat dissipation.
• P = V²/R is best for parallel circuits where every branch has the same voltage — divide V² by each branch resistance for branch power.

The squared-current formula also explains why long-distance power transmission uses high voltage: doubling voltage halves current for the same delivered power, and quartering current quarters the I²R losses in the transmission line. This is the entire reason national grids step up to 110–765 kV for long hauls and step down only at the load end.

Ohm's Law solves countless everyday electrical problems:

• LED current limiting: a 5 V supply powering a red LED (2 V forward voltage, 20 mA desired current) needs R = (5 − 2)/0.02 = 150 Ω.
• Wire sizing: a 20 A circuit at 240 V over 30 m of cable produces voltage drop = I × R_wire; pick a gauge that keeps drop under 3 % (about 7 V on a 240 V circuit, 3.6 V on 120 V).
• Fuse selection: a 12 V supply with a 4 Ω load draws 3 A, so a 5 A fuse provides protection without nuisance trips at startup.
• Battery life: a 9 V alkaline (~500 mAh) powering a 100 Ω load draws 90 mA and runs for ~5.5 hours.
• Space-heater sizing: a 1500 W heater on 120 V draws 12.5 A — needs a 15 A or 20 A circuit; the same heater on 230 V draws only 6.5 A.

Every one of these is one Ohm's Law calculation away.

In a series circuit (components on a single loop), the same current flows through every component, and total resistance is the sum: R_total = R₁ + R₂ + R₃ + …. Voltage divides across components proportionally to their resistance — this is the voltage-divider rule.

Two resistors R₁ and R₂ in series across V_in produce V_out across R₂ equal to V_in × R₂/(R₁ + R₂).

Engineers use this constantly: voltage dividers convert a 12 V battery rail down to 5 V or 3.3 V for sensors, attenuators reduce a strong signal to a measurable level, and pull-up/pull-down resistors set logic-level defaults on microcontroller pins.

Apply V=IR to each resistor individually using the (single, shared) loop current to find the voltage across that specific component.

In a parallel circuit (multiple branches between the same two nodes), every branch has the same voltage across it, and total resistance is the reciprocal sum: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + …. For two resistors in parallel the formula simplifies to R_total = (R₁ × R₂)/(R₁ + R₂).

Currents in each branch are inversely proportional to branch resistance — the lower-resistance branch carries more current. This is why house wiring is parallel: each outlet sees the full mains voltage regardless of what other outlets draw, and turning one appliance on does not dim the others.

Apply V=IR to each branch individually using the (shared) node voltage to find each branch current; total current is the sum of branch currents (Kirchhoff's current law).

Pure resistive AC loads (heaters, incandescent lamps, hairdryers) follow V = IR using RMS values: a 1500 W heater on 230 V_rms draws 6.5 A_rms.

Add capacitors or inductors and resistance generalises to impedance Z, which is frequency-dependent and complex-valued: Z_R = R, Z_C = 1/(2πfC) at -90°, Z_L = 2πfL at +90°. Series and parallel combinations follow the same rules as resistors, but with complex arithmetic.

Real AC power requires the power factor: P_real = V_rms × I_rms × cos(φ), where φ is the phase angle between voltage and current. Resistive loads have PF = 1; motors typically 0.7–0.85 lagging; LED drivers depend on design.

Utilities meter apparent power (V × I) for commercial customers and surcharge low PF — capacitor banks correct it. For everyday domestic Ohm's Law work, you can usually treat PF as 1 and skip the complex math.

Ohm's Law applies strictly to ohmic (linear) materials where resistance stays constant regardless of applied voltage. Most metals and standard resistors qualify within their normal operating range. Many common components do not.

• Diodes and LEDs have exponential voltage-current curves — they block current below a threshold (≈ 0.6 V for silicon diodes, 1.8–3.4 V for LEDs) and then conduct heavily with small voltage increases above that threshold. This is why LEDs need a current-limiting resistor: without one, current would skyrocket the moment the threshold is crossed and the LED would burn out instantly.
• Transistors, MOSFETs, and ICs have elaborate nonlinear behaviour described by Ebers-Moll or square-law equations, not V=IR.
• Incandescent bulbs have temperature-dependent resistance (cold filament ≈ 1/10 of hot resistance — why bulbs often fail at switch-on from inrush current).
• Thermistors deliberately vary resistance with temperature.

For every non-ohmic component, manufacturers provide datasheet curves or piecewise-linear models — Ohm's Law is the wrong tool there.

Three conversions cover most daily needs:

• Watts to amps: I = P/V. A 1500 W heater on 120 V mains draws 1500/120 = 12.5 A; on 230 V it draws 6.5 A.
• Amps to watts: P = V × I. A device pulling 2 A from 12 V uses 24 W.
• Volts to watts: P = V²/R if you know resistance, otherwise you need current too.

Watts and watt-hours are different: watts is power (rate), watt-hours is energy (cumulative). A 100 W bulb left on for 10 hours uses 100 × 10 = 1000 Wh = 1 kWh — your meter measures kWh and electricity bills charge per kWh (typically £0.25 / $0.16 / CA$0.13 / AU$0.30 per kWh in 2026).

Mains voltage worldwide: 120 V (US, Canada, Mexico, Japan parts), 230 V (UK, EU, Australia, NZ, India, most of Africa and Asia). Same Ohm's Law math; just plug in the right voltage.

Wires have resistance — small per metre but cumulative over long runs. Voltage drop = I × R_wire, where R_wire depends on conductor material (copper or aluminium), gauge or cross-section, and length.

Reference values:

• 14 AWG copper ≈ 8.3 mΩ/m
• 12 AWG ≈ 5.2 mΩ/m
• 10 AWG ≈ 3.3 mΩ/m

A 100-foot (30 m) run of 14 AWG copper has about 0.25 Ω total; carrying 15 A drops 3.75 V. On a 120 V circuit that is 3.1 % drop — at the edge of acceptable.

Aim for under 3 % on branch circuits, under 2 % on feeders (NEC US, BS 7671 UK, CSA C22 Canada, AS/NZS 3000 AU all give similar guidance). Long runs to outbuildings or pumps need oversized cable to keep drop within spec. Higher voltage helps quadratically: doubling voltage halves the current for the same load, and quarters the I²R losses.

Six recurring errors:

• Forgetting unit conversion: mixing milliamps with ohms gives volts off by 1000. Either convert mA to A first, or remember the prefix cancellation (mA × kΩ = V exactly).
• Skipping the wattage check: a resistor that passes the right current still burns out if power exceeds its watt rating — always compute P = I²R or P = V²/R and pick a resistor rated at least 2× that.
• Using DC formulas for AC reactive loads without accounting for impedance and power factor.
• Treating non-ohmic components (LEDs, diodes) as resistors — they are not.
• Ignoring temperature: filament bulbs, motors at startup, and high-current resistors all change resistance with temperature.
• Forgetting voltage drop on long wire runs: the load gets less voltage than the supply, the difference being heat in the wire.

Each of these is one calculator click away from being caught.

German physicist Georg Simon Ohm (1789–1854) published 'Die galvanische Kette, mathematisch bearbeitet' (The Galvanic Circuit Investigated Mathematically) in 1827, formalising the proportional relationship between voltage and current that now bears his name.

His work was initially ignored or dismissed by German academics — he was actually demoted at his secondary-school teaching post for the 'unscientific' nature of his findings. The Royal Society of London awarded him the Copley Medal in 1841, finally recognising the importance of the law.

The SI unit of resistance — the ohm (Ω) — was named in his honour at the 1881 International Electrical Congress in Paris.

Modern Ohm's Law is taught identically in school physics curricula across the US (NGSS), UK (GCSE / A-Level), Canada, Australia, and worldwide — one of the few engineering equations as universal as F = ma.