⚡ Ohm's Law Calculator

Instantly calculate Voltage (V), Current (I), Resistance (R) & Power (P) — enter any 2 known values

All 12 Formulas Unit Conversion Free & Instant DC & AC Circuits

⚡ Interactive Ohm's Law Calculator

💡 Instructions: Enter any 2 known values below and click Calculate. The remaining quantities are computed automatically. Leave unknown fields blank.

V Voltage (E)

I Current

Ω Resistance

W Power

Voltage

—

Current

—

Resistance

—

Power

—

💡 Quick Tip: The two master equations are \( V = I \times R \) (Ohm's Law) and \( P = V \times I \) (Watt's Law). All 12 formulas are algebraic rearrangements of these two.

🔵 Ohm's Law Formula Wheel

V \(I \times R\)
\(P \div I\)
\(\sqrt{P \cdot R}\)

I \(V \div R\)
\(P \div V\)
\(\sqrt{P \div R}\)

P \(V \times I\)
\(I^2 R\)
\(V^2 \div R\)

R \(V \div I\)
\(P \div I^2\)
\(V^2 \div P\)

How to use the formula wheel:

Locate your target variable (V, I, R, or P)
Choose the formula that uses your 2 known values
Substitute and solve — the calculator above does this automatically!

The wheel encodes all 12 equations derived from \( V = IR \) and \( P = VI \).

📐 All 12 Ohm's Law Formulas

Find	Formula 1	Formula 2	Formula 3
Voltage (V)	\( V = I \times R \)	\( V = \dfrac{P}{I} \)	\( V = \sqrt{P \times R} \)
Current (I)	\( I = \dfrac{V}{R} \)	\( I = \dfrac{P}{V} \)	\( I = \sqrt{\dfrac{P}{R}} \)
Resistance (R)	\( R = \dfrac{V}{I} \)	\( R = \dfrac{P}{I^2} \)	\( R = \dfrac{V^2}{P} \)
Power (P)	\( P = V \times I \)	\( P = I^2 \times R \)	\( P = \dfrac{V^2}{R} \)

📖 How to Use This Ohm's Law Calculator

1

Identify Your Known Values
Determine which two of the four quantities — Voltage (\(V\)), Current (\(I\)), Resistance (\(R\)), or Power (\(P\)) — you already know from your circuit or problem. You need exactly two to find the other two.
2

Select the Correct Unit
Use the dropdown next to each field to choose the right prefix. For example, select mA for milliamps, kΩ for kilohms, or kV for kilovolts. The calculator handles all conversions to base SI units automatically.
3

Enter Values & Click Calculate
Type your two known numbers into the respective fields and press the ⚡ Calculate button (or hit Enter). Leave unknown fields completely blank — do not type 0.
4

Read Your Results
The result panel shows all four quantities with appropriate unit prefixes (m, k, M) and specifies which formula was applied. Computed fields are highlighted in blue so you can distinguish inputs from outputs.
5

Clear & Recalculate
Click Clear All to reset all fields and start a new calculation. You can also update any field value and press Calculate again without clearing.

🔬 Understanding Ohm's Law — A Complete Guide

Ohm's Law is the foundational principle of electrical engineering and electronics. Formulated by German physicist Georg Simon Ohm in 1827, it describes the precise relationship between three fundamental electrical quantities: Voltage (V), Current (I), and Resistance (R). In its simplest form, the law states:

Ohm's Law

\[ V = I \times R \]

Voltage (V) = Current (A) × Resistance (Ω)

This seemingly simple equation unlocks an entire universe of circuit analysis. Rearranged, it gives us \( I = \frac{V}{R} \) and \( R = \frac{V}{I} \), meaning that if any two of the three are known, the third can always be calculated. This is why Ohm's Law is not just a formula — it is a systematic problem-solving tool used by engineers, electricians, students, and hobbyists worldwide every single day.

What is Voltage?

Voltage (also called electromotive force or potential difference) is the electrical "pressure" that drives current through a circuit. Measured in Volts (V), it represents the energy per unit charge. A 12 V battery pushes electrons with 12 joules of energy per coulomb of charge. Common voltages include: 1.5 V (AA battery), 5 V (USB), 12 V (automotive), 120/230 V (mains AC), and hundreds of kilovolts in power transmission lines.

What is Current?

Current is the rate of flow of electric charge through a conductor, measured in Amperes (A). One ampere equals one coulomb of charge passing a point per second: \( 1\,\text{A} = 1\,\text{C/s} \). Conventional current flows from positive to negative, while electrons physically move in the opposite direction. LEDs typically draw 20 mA, a smartphone charger draws 1–3 A, and a home air conditioner may draw 10–20 A.

What is Resistance?

Resistance is the opposition a material offers to the flow of current, measured in Ohms (Ω). Conductors like copper have very low resistance; insulators like rubber have extremely high resistance. Georg Ohm discovered that for most metallic conductors at constant temperature, resistance remains constant regardless of applied voltage — these are called ohmic materials. Semiconductors and some other devices are non-ohmic (their resistance changes with voltage or current).

⚡

Ohm's Law (V = IR)

The primary relationship between voltage, current, and resistance for any ohmic conductor. Valid for DC circuits and purely resistive AC loads.

💡

Watt's Law (P = VI)

Relates electrical power to voltage and current. Combined with Ohm's Law, this yields all 12 electrical formulas for V, I, R, and P.

🔺

The VIR Triangle

A classic memory aid: place V at the top, I and R at the bottom. Cover the unknown to reveal the formula: V=IR, I=V/R, R=V/I.

🌐

AC Circuits & Impedance

For AC circuits with capacitors or inductors, replace R with impedance Z (measured in Ω): \( V = I \times Z \). Impedance accounts for reactance.

💡 Watt's Law — Understanding Electrical Power

Watt's Law, named after Scottish inventor James Watt, defines electrical power as the product of voltage and current:

Watt's Law

\[ P = V \times I \]

Power (W) = Voltage (V) × Current (A)

By substituting Ohm's Law (\(V = IR\)) into the power equation, we derive two additional power formulas:

\( P = I^2 \times R \) — Power from current and resistance (Joule heating)
\( P = \dfrac{V^2}{R} \) — Power from voltage and resistance

Joule's Law (\(P = I^2 R\)) is particularly important in understanding heat dissipation in resistors, wiring, and electronic components. Every resistor has a maximum power rating (e.g., ¼ W, ½ W, 1 W) — exceeding it causes overheating and failure.

📝 Worked Examples — Step by Step

📌 Example 1 — Finding Current (I)

Given: A 12 V battery connected to a 4 Ω resistor.

Find: Current (I) and Power (P).

Solution:

\[ I = \frac{V}{R} = \frac{12\,\text{V}}{4\,\Omega} = 3\,\text{A} \]

\[ P = V \times I = 12\,\text{V} \times 3\,\text{A} = 36\,\text{W} \]

Answer: The circuit draws 3 A of current and consumes 36 W of power.

📌 Example 2 — Finding Resistance (R)

Given: A 60 W light bulb operating at 120 V.

Find: Resistance (R) and Current (I).

Solution:

\[ I = \frac{P}{V} = \frac{60\,\text{W}}{120\,\text{V}} = 0.5\,\text{A} \]

\[ R = \frac{V}{I} = \frac{120\,\text{V}}{0.5\,\text{A}} = 240\,\Omega \]

Or directly: \[ R = \frac{V^2}{P} = \frac{(120)^2}{60} = \frac{14{,}400}{60} = 240\,\Omega \]

Answer: The bulb's filament has a resistance of 240 Ω at operating temperature.

📌 Example 3 — LED Resistor Calculation

Given: 5 V supply, 2 V LED forward voltage, 20 mA LED current.

Find: Series resistor value and its power rating.

Solution:

\[ R = \frac{V_{\text{supply}} - V_{\text{LED}}}{I} = \frac{5 - 2}{0.02} = \frac{3}{0.02} = 150\,\Omega \]

\[ P_R = I^2 \times R = (0.02)^2 \times 150 = 0.0004 \times 150 = 0.06\,\text{W} \]

Answer: Use a 150 Ω resistor rated for at least 0.06 W (a standard ¼ W resistor is more than adequate).

📌 Example 4 — Power from Resistance & Current

Given: A 10 Ω heating element carries 5 A of current.

Find: Voltage across it and power dissipated.

Solution:

\[ V = I \times R = 5 \times 10 = 50\,\text{V} \]

\[ P = I^2 \times R = 5^2 \times 10 = 25 \times 10 = 250\,\text{W} \]

Answer: The heater drops 50 V and dissipates 250 W.

🔌 Advanced Topics in Ohm's Law

Series Circuits

In a series circuit, resistors are connected end-to-end. The same current flows through every element, and voltages add up. The total resistance is: \[ R_{\text{total}} = R_1 + R_2 + R_3 + \cdots \] Each resistor drops a portion of the total voltage: \( V_n = I \times R_n \). This is applied directly using Ohm's Law.

Parallel Circuits

In a parallel circuit, all resistors share the same voltage but carry different currents. The total resistance satisfies: \[ \frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots \] For two parallel resistors: \( R_{\text{total}} = \dfrac{R_1 \times R_2}{R_1 + R_2} \). Ohm's Law (\(I = V/R\)) is then applied to find current through each branch.

Ohm's Law in AC Circuits — Impedance

For AC circuits containing capacitors and inductors, pure resistance is replaced by impedance (Z), a complex quantity in ohms: \[ Z = \sqrt{R^2 + (X_L - X_C)^2} \] where \( X_L = 2\pi f L \) is inductive reactance and \( X_C = \dfrac{1}{2\pi f C} \) is capacitive reactance. The AC version of Ohm's Law becomes: \[ V_{rms} = I_{rms} \times Z \] For purely resistive loads, \( Z = R \) and the DC formula applies directly.

Three-Phase Power

For 3-phase AC systems (industrial motors, power distribution), the total power formula is: \[ P_{\text{3-phase}} = \sqrt{3} \times V_{LL} \times I_L \times \cos\phi \] where \( V_{LL} \) is the line-to-line voltage, \( I_L \) is the line current, and \( \cos\phi \) is the power factor. Ohm's Law still applies per phase using phase voltage and phase current.

⚠️ Important: Ohm's Law applies only to linear, ohmic devices at constant temperature. Diodes, transistors, thermistors, and incandescent filaments are non-ohmic — their resistance changes with operating conditions and Ohm's Law cannot be applied directly.

📏 Electrical Unit Conversion Reference

Quantity	Unit	Conversion	Symbol
Voltage	Millivolt	\( 1\,\text{mV} = 0.001\,\text{V} \)	mV
Voltage	Kilovolt	\( 1\,\text{kV} = 1{,}000\,\text{V} \)	kV
Current	Microamp	\( 1\,\mu\text{A} = 0.000001\,\text{A} \)	μA
Current	Milliamp	\( 1\,\text{mA} = 0.001\,\text{A} \)	mA
Resistance	Kilohm	\( 1\,\text{k}\Omega = 1{,}000\,\Omega \)	kΩ
Resistance	Megohm	\( 1\,\text{M}\Omega = 1{,}000{,}000\,\Omega \)	MΩ
Power	Milliwatt	\( 1\,\text{mW} = 0.001\,\text{W} \)	mW
Power	Kilowatt	\( 1\,\text{kW} = 1{,}000\,\text{W} \)	kW

🌍 Real-World Applications of Ohm's Law

Ohm's Law is not confined to textbooks — it is applied in virtually every domain that involves electricity:

Home Wiring & Safety: Electricians use \( I = P/V \) to size wiring and circuit breakers. A 2,400 W oven on a 120 V circuit draws \( I = 2400/120 = 20\,\text{A} \), requiring a 20-amp breaker and appropriately rated wire.
Electronics Design: Engineers calculate current-limiting resistors for LEDs, biasing for transistors, and voltage dividers — all using Ohm's Law directly.
Battery Technology: Internal resistance of a battery causes a voltage drop under load. If a battery's internal resistance is 0.5 Ω and it delivers 4 A, the internal drop is \( V = 4 \times 0.5 = 2\,\text{V} \).
Motor Control: The starting current of a DC motor is limited by its armature resistance: \( I_\text{start} = V/R_\text{armature} \). Large motors need soft-starters to prevent excessive inrush currents.
Solar Energy: Ohm's Law governs the I–V characteristic curve of photovoltaic cells, helping engineers find the maximum power point for PV panels.
Medical Devices: ECG machines, defibrillators, and impedance cardiography all rely on Ohm's Law to safely deliver or measure precise electrical quantities through human tissue.
Audio Engineering: Speaker impedance (4 Ω, 8 Ω) and amplifier output power are matched using \( P = V^2/R \) to maximize efficiency and prevent distortion.

Written & Verified by Num8ers Editorial Team — STEM Education Specialists Last updated: April 2026 · Reviewed for accuracy and curriculum alignment

❓ Frequently Asked Questions About Ohm's Law

What is Ohm's Law and what is its formula?

Ohm's Law states that the voltage across a conductor is directly proportional to the current flowing through it, provided temperature and other physical conditions remain constant. The formula is: \( V = I \times R \), where V is voltage in volts, I is current in amperes, and R is resistance in ohms. The law was published by Georg Simon Ohm in 1827.

How do I calculate voltage if I know current and resistance?

Use \( V = I \times R \). Simply multiply the current (in amps) by the resistance (in ohms). Example: If \( I = 3\,\text{A} \) and \( R = 5\,\Omega \), then \( V = 3 \times 5 = 15\,\text{V} \).

How do I calculate current using Ohm's Law?

Use \( I = \dfrac{V}{R} \). Divide the voltage (in volts) by the resistance (in ohms). Example: A 120 V supply through a 60 Ω lamp gives \( I = 120 / 60 = 2\,\text{A} \).

How do I calculate resistance from voltage and current?

Use \( R = \dfrac{V}{I} \). Divide voltage by current. Example: 12 V source driving 2 A of current → \( R = 12 / 2 = 6\,\Omega \).

What are the three forms of Ohm's Law?

The three rearrangements of the core equation are:

\( V = I \times R \) — to find voltage
\( I = V / R \) — to find current
\( R = V / I \) — to find resistance

Combined with Watt's Law (\( P = V \times I + \) substitutions), you get 12 equations in total.

What are the four power formulas in Ohm's Law?

Power can be calculated four ways:

\( P = V \times I \) — voltage times current
\( P = I^2 \times R \) — Joule heating formula
\( P = V^2 / R \) — voltage squared over resistance
\( P = V^2 / R \) (same as above, derived from substitution)

All four are algebraically equivalent under Ohm's Law.

Can Ohm's Law be used for AC circuits?

For purely resistive AC loads (heaters, incandescent bulbs), yes — the formula \( V_{rms} = I_{rms} \times R \) holds exactly. For circuits with capacitors and inductors, resistance is replaced by impedance \( Z \): \( V = I \times Z \). Impedance includes both resistance and reactance and is measured in ohms.

How do I calculate resistor wattage (power rating)?

Use \( P = I^2 \times R \) or \( P = V^2 / R \). Always choose a resistor rated for at least 2× the calculated power for safety. Example: A 100 Ω resistor carrying 50 mA dissipates \( P = (0.05)^2 \times 100 = 0.25\,\text{W} \), so use a ½ W or 1 W resistor.

What is the Ohm's Law triangle and how do I use it?

The VIR triangle is a memory device: draw a triangle with V at the top, I at the bottom left, and R at the bottom right. To find any variable, cover it with your finger:

Cover V: see I × R → multiply Current and Resistance
Cover I: see V/R → divide Voltage by Resistance
Cover R: see V/I → divide Voltage by Current

What is the difference between Ohm's Law and Kirchhoff's Laws?

Ohm's Law relates voltage, current, and resistance across a single component. Kirchhoff's Voltage Law (KVL) states that the sum of all voltages around any closed loop is zero. Kirchhoff's Current Law (KCL) states that the sum of all currents entering a node equals the sum leaving. Together, Ohm's and Kirchhoff's laws are sufficient to solve any DC linear circuit.

When does Ohm's Law NOT apply?

Ohm's Law does not apply to non-ohmic (non-linear) devices:

Diodes & LEDs — have a non-linear I–V curve
Zener diodes — clamp voltage at a fixed level
Transistors — current is controlled by a gate/base signal
Thermistors — resistance changes significantly with temperature
Superconductors — zero resistance below a critical temperature

For these, more advanced models (Shockley diode equation, transistor models) are needed.

What is the unit of resistance and who is it named after?

The unit of electrical resistance is the ohm (Ω), named after Georg Simon Ohm (1789–1854), the German physicist and mathematician who discovered the proportional relationship between voltage and current. The symbol Ω is the Greek letter omega, adopted by the International Electrotechnical Commission (IEC) as the standard symbol.

How do I convert milliamps to amps for Ohm's Law calculations?

Divide by 1,000: \( 1\,\text{mA} = 0.001\,\text{A} \). So 500 mA = 0.5 A. Always convert to base SI units before applying Ohm's Law formulas to ensure consistent results. Our calculator handles this conversion automatically via the unit dropdown.

What is the relationship between Ohm's Law and Joule's Law?

Joule's Law states that the heat produced in a resistor is proportional to the square of the current: \( P = I^2 \times R \). This is derived by substituting \( V = IR \) into \( P = VI \). Joule's Law explains why high-current wires must be thick (lower R) to minimize heat loss, and why fuses and circuit breakers protect circuits by interrupting excessive current.

What resistor do I need to limit current to an LED?

Use: \( R = \dfrac{V_{\text{supply}} - V_f}{I_f} \), where \( V_f \) is the LED's forward voltage (typically 1.8–3.3 V) and \( I_f \) is the desired forward current (typically 10–30 mA). Example: 5 V supply, red LED (Vf = 2 V, If = 20 mA): \( R = (5 - 2) / 0.02 = 150\,\Omega \). Choose the next standard value ≥ 150 Ω.

How does resistance change with temperature?

For most metals, resistance increases with temperature. The formula is: \( R_T = R_0 \times [1 + \alpha(T - T_0)] \) where \( \alpha \) is the temperature coefficient of resistance (e.g., copper α ≈ 0.00393 /°C). This is why incandescent bulbs have much higher resistance when hot than when cold — their cold resistance is much lower, causing a brief current surge when switched on.

How accurate is the Num8ers Ohm's Law Calculator?

The calculator uses JavaScript's IEEE 754 double-precision floating point, providing approximately 15–16 significant digits of precision. For practical electrical and electronics work, this far exceeds the tolerance of real components (typically ±1%–±10%). No internet connection is required after the page loads; all calculations happen instantly in your browser.

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