Ohm's Law Calculator

Ohm's law states that voltage equals current times resistance: V = I × R. Rearranged to find resistance, R = V ÷ I. So 12 volts driving 2 amps means a resistance of 12 ÷ 2 = 6 ohms. The power dissipated is P = V × I = 12 × 2 = 24 watts. The calculator above solves resistance and power from any voltage and current you enter.

Ohm's law is the single most important equation in electronics and electrical work. It ties together the three fundamental quantities — voltage (electrical pressure), current (flow of charge), and resistance (opposition to flow) — and, combined with the power law P = V × I, it lets you find any of these values when you know two others. Master these two equations and you can analyze virtually any DC or resistive circuit.

Two equations, and their rearrangements, cover everything:

The four quantities are:

• Voltage (V), in volts — the potential difference, or electrical "pressure," driving current.
• Current (I), in amperes — the rate of charge flow.
• Resistance (R), in ohms (Ω) — opposition to current; higher resistance means less current for a given voltage.
• Power (P), in watts — the rate of energy conversion into heat, light, or work.

Combining the two laws yields useful hybrids: P = I²R (power from current and resistance) and P = V²/R (power from voltage and resistance). These twelve rearrangements form the classic "Ohm's law wheel." For the full conceptual treatment with analogies and worked derivations, read Ohm's law explained.

These examples show the law solving real circuit questions.

Example 1 — Automotive bulb: A 12 V system drives 2 A through a bulb. Resistance = 12 ÷ 2 = 6 Ω. Power = 12 × 2 = 24 W. Cross-check with I²R: 2² × 6 = 24 W. ✓

Example 2 — Household heater element: A 120 V circuit draws 10 A. Resistance = 120 ÷ 10 = 12 Ω. Power = 120 × 10 = 1,200 W. Using V²/R: 120² ÷ 12 = 14,400 ÷ 12 = 1,200 W. ✓

Example 3 — LED with series resistor: To drop 3 V across a resistor while allowing 20 mA (0.02 A), resistance = 3 ÷ 0.02 = 150 Ω. The resistor dissipates 3 × 0.02 = 0.06 W, so a 1/8 W resistor is fine.

Example 4 — Finding current: A 9 V battery across a 470 Ω resistor pushes I = 9 ÷ 470 = 0.0191 A (19.1 mA), dissipating 9 × 0.0191 = 0.17 W. This is why quarter-watt resistors are standard for low-voltage electronics — the dissipation almost always stays well under their rating, leaving a comfortable thermal margin.

Ohm's law connects directly to power dissipation and heat, which drives component and conductor sizing. The three power formulas are equivalent but each is useful in different situations:

• P = V × I — when you know voltage and current directly.
• P = I² × R — when you know current and resistance; this form reveals why doubling current quadruples heating.
• P = V² ÷ R — when you know voltage and resistance; used for heating elements at fixed supply voltage.

The I²R form explains conductor heating and voltage drop: because power loss rises with the square of current, high-current circuits lose disproportionately more energy in wiring. This is precisely why higher-voltage distribution (which carries less current for the same power) is more efficient over distance — the same principle behind the 3-phase power calculator and long-distance transmission. It is also why you must size wire for the current it carries; excessive I²R heating is a fire risk.

To move from these resistive-circuit fundamentals into applied power conversions, use the watts to volts calculator, the volts to watts calculator, and the watts to amps calculator.

Ohm's law in its simple form, V = I × R, applies exactly to DC circuits and purely resistive AC loads (heaters, incandescent lamps). For AC circuits containing inductance or capacitance, resistance (R) is replaced by impedance (Z), and the law becomes V = I × Z.

Impedance combines resistance with reactance — the frequency-dependent opposition from inductors and capacitors. Because reactance shifts the current out of phase with the voltage, AC power calculations also introduce power factor (the cosine of that phase angle). This is why an AC motor's real power is V × I × PF, not simply V × I.

For everyday DC work — batteries, automotive systems, electronics, LED circuits — the pure resistance form used by this calculator is exactly right. When you move to reactive AC loads, pair Ohm's law with power-factor-aware tools like the volts to watts calculator and the 3-phase power calculator, and see the deeper discussion in Ohm's law explained.

1. Enter the voltage in volts. Use the potential difference across the component or circuit segment you are analyzing.
2. Enter the current in amps. Use the measured or intended current through that same component. For milliamps, convert to amps (20 mA = 0.02 A).
3. Read the resistance. The primary result is R = V ÷ I in ohms — the resistance that produces that current at that voltage.
4. Check the power. The calculator also shows power (V × I), conductance, and an I²R cross-check so you can confirm the numbers are consistent.

The result updates live. Use it to choose a series resistor, verify a component's resistance, size a heating element, calculate the voltage drop across a cable, or sanity-check a bench measurement before trusting it.

Ohm's law is the workhorse of electrical and electronic design:

Electronics and PCB design. Choosing current-limiting resistors for LEDs, setting bias points, and calculating voltage dividers all rely on R = V ÷ I. It is the first law every technician learns.

Wire and fuse sizing. Knowing the current and the conductor's resistance reveals voltage drop and I²R heating, which determine safe wire gauge and fuse ratings.

Troubleshooting. Measuring two of voltage, current, and resistance and computing the third quickly locates shorts (low resistance, high current) and opens (high resistance, no current).

Heating elements and loads. Toasters, kettles, and industrial heaters are designed around P = V²/R, selecting the element resistance to deliver the target wattage at the supply voltage. This connects directly to energy use via the watts to kWh calculator.

Battery and solar systems. Ohm's law governs charge controllers, current-sense resistors, and the voltage drop across long cable runs between panels, batteries, and loads. A run of undersized wire behaves as an unwanted series resistance: the current through it, times that resistance, is the voltage lost before power ever reaches the load, and the square of that current times the resistance is heat wasted in the cable. Applying R = V ÷ I to a measured drop reveals hidden connection or conductor resistance, and it is why installers size cable to keep resistive losses to a small percentage of system voltage.

Real circuits combine multiple resistances, and Ohm's law extends cleanly to both series and parallel arrangements. Knowing how resistances add lets you find the total current, the voltage across each part, and the power in each component.

Series circuits (components end-to-end) share the same current, and their resistances add: R_total = R1 + R2 + R3. The voltage divides in proportion to each resistance — a larger resistor drops more voltage. For example, a 6 Ω and a 4 Ω resistor in series across 12 V total 10 Ω, drawing 12 ÷ 10 = 1.2 A. The 6 Ω resistor drops 6 × 1.2 = 7.2 V and the 4 Ω drops 4.8 V, and the two add back to the 12 V supply — a useful check.

Parallel circuits (components across the same two nodes) share the same voltage, and their conductances add, so the combined resistance is always less than the smallest branch: 1 ÷ R_total = 1/R1 + 1/R2. Two 6 Ω resistors in parallel give 3 Ω; across 12 V they draw 12 ÷ 3 = 4 A total, split as 2 A per branch. Because each branch sees the full voltage, adding parallel paths increases total current and total power draw — which is exactly how household outlets on one circuit accumulate load toward the breaker limit.

These rules, combined with the power law, let you analyze any resistive network: reduce it to an equivalent resistance, find the total current with I = V ÷ R, then work back to individual voltages and currents. Voltage dividers, current-limiting networks, and sensor circuits all rely on this. Once you move from resistive networks to power delivery and distribution, the same current-versus-voltage trade-offs reappear in the 3-phase power calculator and the watts to amps calculator.

• Mixing units. Keep volts, amps, and ohms consistent. Milliamps and kilohms are common trip-ups — convert to base units first (or work consistently in mA and kΩ, which also cancel correctly).
• Applying pure resistance to reactive AC. Inductive and capacitive AC loads need impedance (Z) and power factor, not simple resistance.
• Ignoring power ratings. A resistor with the right ohms can still fail if it must dissipate more watts than its rating; always check P = I²R.
• Assuming constant resistance. Many materials change resistance with temperature; a cold heating element or lamp filament has much lower resistance than when hot.
• Dividing by zero current. Resistance is undefined at zero current; you need a real current value to solve for R.

For applied conversions built on these fundamentals, use the watts to volts calculator, the watts to amps calculator, and the amps to kW calculator.