Ohm's Law Calculator

Ohm's Law Calculator solves voltage, current, resistance and power from any two values, then picks the nearest stocked resistor value and a wattage rating with margin for the heat.

The 12 Formulas Behind the Ohm's Law Calculator

Ohm's law says the current through a conductor is directly proportional to the voltage across it. Tony Kuphaldt's Lessons in Electric Circuits states it that way and gives the three Ohm's law formulas that follow from it. Each one solves for a different quantity.

$$V=I\times R$$

$$I=\frac{V}{R}$$

$$R=\frac{V}{I}$$

V is voltage in volts, I is current in amps and R is resistance in ohms. To calculate Ohm's law by hand, cover the unknown and combine the other two. The textbook's own example is a 12 V battery across 3 Ω, which drives 12 ÷ 3, or 4 A.

The Ohm's Law Calculator adds power as a fourth quantity, so any two known values give the other two. Six pairings are offered in the Known Values menu. The default pairing is 12 V and 2 A, which returns 6 Ω and 24 W from R = V ÷ I and P = V × I.

The Ohm's Law Wheel panel then writes out all twelve formulas with those numbers. The two rows used for the answer are highlighted, and the other ten work as a cross-check.

Entries accept millivolts to kilovolts, microamps to amps, milliohms to megohms, and milliwatts, watts, kilowatts or horsepower. The page runs in a phone browser, so it does the job of an Ohm's Law Calculator app with nothing to install.

Watt's Law and the Three Power Formulas

The power relation P = V × I is often called Watt's law. Swapping V or I for its Ohm's law equivalent gives the three formulas of power, which is why the tool doubles as a Watt's law calculator.

$$P=V\times I$$

$$P=I^2\times R$$

$$P=\frac{V^2}{R}$$

An amp is not equal to a watt, because watts also depend on voltage. A 20 A load is 2,400 W on a 120 V circuit, 4,800 W on 240 V and only 240 W on a 12 V battery. The Ohm's Law Calculator in Voltage and Current mode shows the 120 V case as a 6 Ω load.

Going from watts to amps divides by the voltage. A 5,000 W heater draws 41.67 A at 120 V and 20.83 A at 240 V, with element resistances of 2.88 Ω and 11.52 Ω. The Current Calculator runs the same sum for single-phase and three-phase supplies.

All of that power leaves a resistance as heat. The fourth result card converts it, so 24 W reads as 81.89 BTU/h and 0.03218 mechanical horsepower. NIST lists one horsepower as 745.6999 W and one BTU per hour as 0.2930711 W in its table of conversion factors.

Ohms to Volts and Ohms to Amps

Ohms do not convert to volts or amps on their own. A second value is always needed, which is why the Ohm's Law Calculator asks for two. As an ohms to volts calculator it multiplies resistance by current, so 100 Ω carrying 50 mA drops 5 V.

As an ohms to amps calculator it divides voltage by resistance. A 100 Ω resistor across 12 V passes 120 mA and dissipates 1.44 W. That is the direct answer to how to calculate amps when the voltage and resistance are known.

Converting volts to ohms works the other way. Divide the voltage by the current, or square the voltage and divide by the power. A 12 V lamp rated 60 W therefore has a hot resistance of 144 ÷ 60, or 2.4 Ω, and draws 5 A.

The same division sizes wiring losses. A cable with 0.1 Ω of resistance carrying 20 A drops 2 V along its length, and the Voltage Drop Calculator covers that case for a full wire run.

What 1 Ohm, 100 Ohms and 1 Kilohm Mean

One ohm is the resistance that lets one amp flow when one volt is applied. NIST's guide to the SI writes the ohm as V/A, the volt as W/A and the siemens of conductance as A/V. So an ohm is not equal to a volt or to an amp. It is the number of volts per amp, and ohms per volt is one over the current, which is 0.5 for a 2 A load.

The prefixes change the size by thousands. One kilohm is 1,000 Ω and one megohm, written 1 MΩ, is 1,000,000 Ω. A lowercase m means milli, so 1 mΩ is 0.001 Ω. Ten ohms is simply 10 Ω, or 0.01 kΩ, and 100 ohms is 0.1 kΩ.

A 1 ohm resistor drops exactly 1 V for every amp through it, which makes a current easy to read as a voltage across it. A familiar part with 100 ohm resistance is the Pt100 temperature sensor. TC Direct's Pt100 specification page gives it 100.00 Ω at 0 °C under IEC 60751.

The fourth card of the Ohm's Law Calculator also shows conductance, which is one divided by resistance. The 6 Ω default reads 166.7 mS, and a 100 Ω part reads 10 mS. One amp of current is one coulomb of charge passing a point each second, and one volt is one watt per amp.

From a Solved Value to a Real Resistor

A solved resistance is rarely a value that can be bought. Resistors come in the E-series steps of IEC 60063, listed in Vishay's table of standard series values. E12 has 12 values per decade and E24 has 24. EEPower's resistor guide pairs E12 with 10% tolerance, E24 with 5% and E96 with 1%.

The first result card of the Ohm's Law Calculator rounds to the nearest step in the chosen series and reruns the circuit at the same voltage. For the 6 Ω default the nearest E24 value is 6.2 Ω, which passes 1.935 A and dissipates 23.23 W.

The second card picks a wattage. The Ohm's Law Calculator takes twice the dissipation and moves up to the next stocked rating, from 1/8 W through 100 W. For 24 W that is a 50 W part with 52% headroom. EEPower's power rating page notes that ratings are usually quoted at 70 °C and fall above that temperature.

SparkFun's resistor tutorial gives a small-signal case. A red LED with a 1.8 V forward voltage on a 9 V battery at 10 mA leaves 7.2 V across the resistor, so it needs about 720 Ω. An LED is not a fixed resistance, so the law is applied to the resistor in series with it.

Entering 7.2 V and 10 mA in the Ohm's Law Calculator returns 720 Ω and 72 mW. The nearest E24 part is 750 Ω, which sets 9.6 mA, and the nearest E12 part is 680 Ω at 10.59 mA. Twice 72 mW is 144 mW, so the card lands on a 1/4 W resistor with 71.2% headroom.

The Same Load at Other Voltages

With resistance fixed, current follows voltage and power follows its square. The third card of the Ohm's Law Calculator shows this for the solved load. The 6 Ω default draws 4 A and 96 W if the voltage doubles to 24 V, and 1 A if it halves to 6 V.

The This Resistance at Common Voltages panel carries the same 6 Ω across nine supplies. It runs from a 1.5 V cell to a 240 V circuit, and the heat climbs from under half a watt to 9.6 kW.

A part that is safe on 12 V can burn on 24 V, because four times the heat lands in the same body. When that heat sits in a transistor or regulator instead of a resistor, the Heat Sink Calculator turns the watts into a required thermal resistance.

Series and Parallel Circuits

For series and parallel circuits, Ohm's law is applied twice. The first pass uses the total resistance to find the supply current. The second pass uses each resistor's own voltage or current. Series resistances add.

$$R_T=R_1+R_2$$

Two 100 Ω resistors in series make 200 Ω. On 12 V the Ohm's Law Calculator gives 60 mA and 0.72 W for the pair. Each resistor then carries 60 mA, drops 6 V and dissipates 0.36 W, which is how a voltage divider splits a supply.

$$\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}$$

For parallel circuits the reciprocals add. The same two resistors in parallel make 50 Ω, and on 12 V the total is 240 mA and 2.88 W. Each branch sees the full 12 V and takes 120 mA. The Parallel Resistor Calculator finds the combined value for longer strings, and that value goes into the Ohm's Law Calculator as the resistance.

AC and 3 Phase Loads

The note under the Ohm's Law Calculator results states the limit of the law. It holds for DC and for resistive AC loads such as heaters and incandescent lamps, entered as RMS values. The RMS Voltage Calculator finds that RMS figure for an AC waveform.

Motors, coils and capacitors on AC also need impedance and power factor, so V × I overstates their real power. On a 3 phase supply the Ohm's Law Calculator still applies to each resistive phase, and the total uses the line values.

$$P=\sqrt{3}\times V_L\times I_L\times PF$$

A balanced resistive load drawing 10 A per line at 480 V has a power factor of 1 and takes 8,314 W. In a wye connection each element sees 277 V, so its resistance is 27.7 Ω. The Three-Phase Power Calculator handles loads with a power factor below 1.

Why the Unit Is Called the Ohm

The ohm is named after Georg Simon Ohm, born in Erlangen, Bavaria, in 1789. Britannica dates his statement of the law to the 1827 book Die galvanische Kette, mathematisch bearbeitet, or The Galvanic Circuit Investigated Mathematically. He received the Royal Society's Copley Medal in 1841 and died in Munich in 1854.

Questions about Ohm's first law or the three Ohm's laws point to one relationship written three ways, V = I × R, I = V ÷ R and R = V ÷ I. Adding P = V × I covers most searches for the three formulas of electricity, and the Ohm's Law Calculator solves all of them from two entries.