Ohm's Law Calculator — V=IR with Power, LED, Divider & Series / Parallel / Mixed Networks

What Ohm's Law actually says

Ohm's Law describes how three fundamental electrical quantities relate. Voltage is the electrical pressure pushing charge through a circuit. Current is the rate at which charge actually flows. Resistance is everything in the path that impedes that flow. Written as one line: V = I × R. Georg Simon Ohm established the relationship experimentally in 1827, and it has been the foundation of every circuit calculation since.

Joule's Law adds a fourth quantity: power. Power is the rate at which electrical energy is converted into heat, light, motion, or sound — measured in watts. It equals voltage times current: P = V × I. Combine the two laws algebraically and you get twelve different formulas, all of which are covered by this calculator.

The reason Ohm's Law is so widely used is that it is the only equation in basic electronics that ties three physically measurable quantities together with a single multiplication. If you know any two of voltage, current, or resistance, the third is a one-step calculation. Combined with Joule's Law, the same logic extends to power, giving you four different quantities you can solve from any two.

The three fundamental quantities explained

Voltage (V) — electrical pressure

Voltage is the difference in electrical potential between two points. It is measured in volts and given the symbol V (or sometimes E, for electromotive force). A 9 V battery has 9 joules of potential energy per coulomb of charge — meaning every coulomb of charge that moves from one terminal to the other gains or loses 9 joules of energy.

The hydraulic analogy is the most useful one for beginners. Think of voltage as water pressure. A taller water tower produces more pressure at the tap. A larger battery produces more voltage. Just as pressure alone does not tell you how much water will flow (you also need to know the pipe diameter), voltage alone does not tell you the current — you need resistance too.

Voltage is always measured between two points, never at a single point. This is why a voltmeter has two probes. The reading tells you the potential difference between wherever the red probe is touching and wherever the black probe is touching.

Current (I) — the flow of charge

Current is the rate at which electrical charge flows through a conductor. It is measured in amperes (amps) and given the symbol I — from the French intensité du courant, because C is already used for capacitance. One amp equals one coulomb of charge passing any point in the circuit per second.

Continuing the water analogy, current is the volume of water flowing per second. More pressure (voltage) or a wider pipe (lower resistance) means more flow (higher current). Current is what actually does work — it lights lamps, turns motors, and heats elements. Voltage alone cannot do any of that; it needs current to flow.

Current is measured in series with the circuit. To measure it, the current must physically flow through the ammeter. This is why placing an ammeter across a voltage source (in parallel) will usually blow its internal fuse — it becomes a near short circuit.

Resistance (R) — opposition to current

Resistance is the opposition a material offers to the flow of current. It is measured in ohms (Ω) and given the symbol R. One ohm is the resistance that allows exactly one amp to flow when exactly one volt is applied across it.

Resistance comes from the physical interactions between moving charges and the atoms of the conductor. As electrons move through a wire, they collide with the atoms and lose energy as heat. Different materials have different resistivities: copper and silver have very low resistivity (good conductors), while rubber and glass have extremely high resistivity (insulators). The resistance of a specific piece of wire also depends on its length and cross-sectional area — twice as long means twice the resistance, twice as thick means half the resistance.

Resistors are components deliberately manufactured to have a specific, stable resistance. Common values range from milliohms (for current sensing) up to megaohms (for pull-up and pull-down networks).

Power — the fourth quantity

Power measures the rate at which electrical energy is converted into another form. It is measured in watts (W). One watt equals one joule per second. This is the quantity that actually determines whether a component is safe — a resistor rated for 0.25 W will overheat if you push 1 W through it, even if the voltage and current individually look reasonable.

Joule's Law gives power in terms of voltage and current: P = V × I. Combining this with Ohm's Law gives two more useful forms:

Which one to use depends on what you already know. If you know voltage and current, use P = V × I. If you know current and resistance, use P = I² × R — this is the version most useful for resistor sizing. If you know voltage and resistance, use P = V² ÷ R. All three give identical results for any correct set of values, and this calculator uses the appropriate one automatically.

Power is not the same as energy. Power is a rate — how fast energy is being transferred. Energy is the total amount transferred. If you run a 1,000 W heater for one hour, you use 1 kilowatt-hour (kWh) of energy. Your electricity bill is measured in kWh, not in watts, which is why running a 100 W bulb for 10 hours costs the same as running a 1,000 W heater for 1 hour.

How to use the calculator

Ohm's Law tab

1. Type a number into any two of the four rows (V, I, R, P). Pick a unit prefix from the dropdown on the right.
2. The result banner at the top updates live. Inputs you typed get a blue INPUT badge; values the tool computed get a green SOLVED badge.
3. Change any input value at any time — the tool remembers the two most recently edited rows and uses them as your primary inputs.
4. Enter a third value to cross-check — the tool warns you if the three do not agree.
5. The formula strip below the inputs shows the exact equation with your numbers plugged in.
6. Click any tile to copy its full-precision value.

LED Resistor tab

Click a colour preset to load its typical forward voltage, then adjust supply and current. The tool returns the exact resistance, nearest E24 standard, resistor power dissipation, and actual current. This is the single most common practical use of Ohm's Law in hobby electronics.

Voltage Divider tab

Enter Vin, R1, and R2. The tool returns output voltage, divider ratio, chain current, and total power. Use this for sensor voltage scaling, reference voltages, and any application where you need a fraction of a larger voltage.

Networks tab

Three modes: Series, Parallel, and Mixed. Enter an optional supply voltage to see the current and power dissipated in each resistor. The colour of each resistor in the diagram reflects its actual power dissipation — blue is safe, red means overheating risk.

All twelve formulas

The Ohm's Law triangle — and its limits

The Ohm's Law triangle is the standard memory aid taught in every introductory electronics course. Draw a triangle with V at the top, and I and R at the bottom corners. Cover the value you want to find:

• Cover V and the remaining symbols are side-by-side (I and R), so you multiply them: V = I × R.
• Cover I and you get V over R, so you divide: I = V ÷ R.
• Cover R and you get V over I, so you divide: R = V ÷ I.

The power triangle works the same way with P at the top and V and I at the bottom. Cover P to multiply, cover V or I to divide.

⚠ The triangle cannot solve everything. Six of the twelve formulas involve square roots (V = √(P × R), I = √(P ÷ R)) — the triangle has no way to represent these. If you only know power and resistance, the triangle is useless. This is why the twelve-formula wheel shown in the calculator exists, and why a proper calculator is more useful than a memory aid.

Worked examples from real scenarios

Example 1 — Current from voltage and resistance

A 9 V battery is connected across a 470 Ω resistor. What current flows?

0.172 W is within the 0.25 W rating of a standard quarter-watt resistor, but close enough that a half-watt part would be safer in a warm enclosure.

Example 2 — Resistor for an LED

You want to drive a red LED (forward voltage 2.0 V, target current 20 mA) from a 5 V supply.

60 mW is well within a standard quarter-watt resistor. For LEDs running continuously in a warm enclosure, the tool would still suggest a half-watt part for thermal margin.

Example 3 — Power dissipated in a resistor

Known: I = 0.1 A, R = 100 Ω. What is the power dissipation?

A 1 W resistor run at 100% of its rating will get very hot. Choose a 2 W or 3 W part for reliability.

Example 4 — Voltage from power and current

A 60 W bulb drawing 0.5 A. What voltage is it running at?

This is the classic US mains voltage. The bulb's filament has about 240 Ω of resistance when hot (it is much lower when cold, which is why incandescent bulbs have a large inrush current).

Example 5 — Square root formulas (power and resistance)

A 4 W, 100 Ω power resistor — what is the maximum safe voltage and current?

This case cannot be solved with the triangle — only the twelve-formula wheel covers it.

Example 6 — Series resistors

Three resistors in series: 100 Ω + 220 Ω + 470 Ω. What is the total resistance?

Example 7 — Parallel resistors

Two resistors in parallel: 100 Ω and 200 Ω. What is the equivalent resistance?

The parallel total is always smaller than the smallest individual resistor — a useful sanity check.

Example 8 — Voltage divider

12 V input, R1 = 10 kΩ, R2 = 4.7 kΩ. What is Vout?

Example 9 — Cross-check with all four quantities

Known: V = 24 V, I = 2 A. Verify P and R using three independent formulas.

All three power formulas give the same answer, which is the strongest consistency check you can do.

Example 10 — LED with calculated resistor

Blue LED (Vf = 3.2 V) from a 5 V supply, 15 mA target.

Example 11 — Electric kettle on 230 V mains

2,000 W kettle. What current and resistance?

Example 12 — Car starter motor

A car starter motor draws roughly 200 A at 12 V during cranking.

This is why starter cables are thick (typically 25–50 mm²) — the wire resistance must be a small fraction of the motor's 0.06 Ω, or the motor will not receive enough voltage to turn.

Example 13 — Reverse: find current from measured voltages

An unknown LED connected to a 5 V supply through a 220 Ω resistor shows a voltage drop of 2.1 V across the LED. What current flows?

Example 14 — Reverse: find resistance from dissipated power

A resistor known to dissipate 2 W at a measured voltage of 20 V. What is its resistance?

Example 15 — Reverse: find current from power and resistance

A 25 Ω heating element rated for 100 W. What current does it draw?

Ohm's Law in AC circuits

Ohm's Law was formulated for DC circuits, but it also applies to AC circuits under specific conditions. The important distinction is whether the load is resistive or reactive.

Purely resistive AC loads

Electric heaters, incandescent lamps, resistive heating elements — these follow Ohm's Law exactly, provided you use RMS (root-mean-square) voltage and current. A 230 V RMS mains supply has a peak voltage of about 325 V, but the RMS value is what you use in V = I × R. This is because RMS is defined as the DC voltage that would deliver the same average power to a resistive load.

Reactive AC loads

Motors, transformers, relays with coils, and anything containing a capacitor or inductor — these do not follow Ohm's Law in its simple form. In these circuits, opposition to current flow is impedance (Z), not resistance. Impedance combines resistance with reactance using vector addition:

where X is reactance in ohms. Ohm's Law becomes V = I × Z, and power is no longer simply V × I but P = V × I × cos(φ), where cos(φ) is the power factor. This is why industrial electricity bills often include a power-factor penalty — a low-power-factor load draws more current than its actual wattage suggests.

Devices that do not obey Ohm's Law

Ohm's Law applies to ohmic or linear devices — components whose resistance stays constant as voltage and current vary. Many real devices are not ohmic:

• Diodes — including LEDs and rectifier diodes. Their resistance drops sharply above the forward-voltage threshold, so current rises exponentially with voltage.
• Thermistors — resistors whose resistance changes with temperature. An NTC thermistor's resistance falls as it warms; a PTC thermistor's resistance rises.
• Filament lamps — a bulb has much lower resistance when cold than when hot. The initial inrush current when you flip the switch can be ten times the steady-state current.
• Varistors (MOVs) — used for surge protection. Their resistance is very high at normal voltages and very low at surge voltages.
• Transistors — collector current depends on base current, not just collector-emitter voltage. Ohm's Law is applied to the surrounding resistors, not to the transistor itself.

⚠ Important for beginners. Never connect an LED directly across a voltage source. Without a series resistor, the current will be limited only by the internal resistance of the source and the LED's own dynamic resistance — usually far too much, and the LED will burn out in seconds. Always use the LED Resistor tab in this calculator to compute a safe series resistor before connecting an LED.

Resistor power ratings and safety

A resistor's wattage rating is the maximum power it can dissipate continuously without exceeding its rated temperature. Exceeding this value causes the resistor to drift in value, crack, or fail open. Standard through-hole resistors are 0.25 W; power resistors go up to 5 W, 10 W, or higher.

Practical guidelines for choosing a wattage rating:

• Derate by 2× if the resistor will run continuously. A calculation showing 0.5 W needs a 1 W resistor, not a 0.5 W one.
• Derate further in hot environments. A resistor rated 0.25 W at 25 °C is often only rated 0.1 W at 70 °C. Inside an enclosure, ambient temperature rises fast.
• Watch the voltage limit. Even a high-wattage resistor has a maximum voltage rating (typically 200–350 V for through-hole parts). High-voltage circuits need resistors specifically rated for the voltage.
• Do not stack the same resistor. If you need 5 W, buy a 5 W resistor — do not assume four 1 W resistors stacked together will work unless you have considered the thermal path.

Temperature effects on resistance

Every conductor's resistance changes with temperature. For most metals, resistance increases as temperature rises, because the atoms vibrate more and scatter moving electrons more often. The relationship is approximated by:

where α is the temperature coefficient of resistance, R₀ is the resistance at the reference temperature T₀ (usually 20 °C), and R(T) is the resistance at the operating temperature T. Copper has α ≈ 0.0039 per °C — a wire at 100 °C has about 30% more resistance than at 20 °C.

For everyday circuit work, resistor drift with temperature is small enough to ignore: a metal-film resistor has α ≈ 0.00005 per °C, so a 50 °C rise changes the value by only 0.25%. But for precision circuits (measurement, instrumentation, or RF), temperature drift is a critical design parameter.

Standard resistor values (E-series)

Resistors are not manufactured in every possible value. The IEC 60063 standard defines the E-series of preferred numbers: E6, E12, E24, E48, E96, E192. The E-number indicates how many values exist per decade — E24 has 24 values per decade, spaced so that adjacent values differ by about 10% (2 values apart), which matches the tolerance of ±5% resistors so that tolerance bands just touch.

Practical implications:

• Hobbyist through-hole resistors are usually E24 (values like 100, 110, 120, 130, 150, 160, 180, 200 Ω…).
• Precision surface-mount resistors are usually E96 (±1% tolerance) with much closer spacing.
• The nearest standard value to any calculation is what you can actually buy — this is why the LED tab in this calculator shows the nearest E24 value alongside the exact value.

Resistor color code

Through-hole resistors use coloured bands to encode their value and tolerance. A typical 4-band resistor is read as: digit, digit, multiplier, tolerance. Five-band resistors add an extra significant digit; six-band resistors add a temperature coefficient.

Example: brown, black, red, gold. Brown = 1, black = 0, red = ×100, gold = ±5%. So the resistor is 10 × 100 = 1,000 Ω = 1 kΩ, with ±5% tolerance. Reading this from the reference table above is faster than trying to memorise all ten colours.

Wire gauge and current capacity

Wires have resistance too, and it matters at high currents. A typical 22 AWG hookup wire has a resistance of about 5.3 Ω per 100 metres. For a 1 A load, that is a 5.3 mV drop per metre of wire — negligible. For a 10 A load, the same wire drops 53 mV per metre and dissipates 0.53 W per metre as heat, which will eventually melt the insulation.

The AWG (American Wire Gauge) system defines standard wire diameters. Higher AWG numbers mean thinner wire. The reference table above lists ampacity (safe current-carrying capacity) for common sizes. When in doubt, size wire for the current you expect and add 25% headroom.

Where Ohm's Law is used

• Hobby electronics — sizing LED resistors, choosing pull-up values, estimating battery life.
• Electrical engineering — circuit design, power distribution, motor sizing, transformer selection.
• Automotive — fuse sizing, wiring gauge, load calculations for lights, motors, and accessories.
• Industrial control — sensor interface design, 4–20 mA loop calculations, PLC wiring.
• Home wiring — voltage drop over long cable runs, breaker sizing, load calculation.
• Test and measurement — designing voltage dividers for multimeter inputs, current shunts for oscilloscope probes.
• Renewable energy — solar panel sizing, battery bank design, inverter load calculation.
• Teaching and exams — every introductory physics and electronics course builds on Ohm's Law.

Measuring V, I, and R with a multimeter

The calculator is a tool for prediction — a multimeter is a tool for verification. In practice, you use both together: calculate what you expect, measure what you actually get, and investigate any discrepancy.

• Measuring voltage. Set the meter to DC volts (or AC volts for mains). Touch the black probe to the negative side of the circuit and the red probe to the positive side of the component you are measuring. The meter is placed in parallel with the component.
• Measuring current. Set the meter to DC amps or milliamps. You must break the circuit and insert the meter in series — current has to flow through the meter. This is the single most dangerous measurement, because a meter set to current and accidentally placed across a voltage source will blow its fuse.
• Measuring resistance. Turn off the circuit and disconnect the component (or at least one of its leads). Set the meter to ohms and touch the probes to the two ends of the resistor. Measuring resistance in-circuit is unreliable because parallel paths distort the reading.

Common mistakes and how to avoid them

• Forgetting to convert milliamps to amps. This is the single most common error. 20 mA must be 0.020 A in the formula. A factor-of-1,000 error is invisible in the numbers but the circuit will not work.
• Mixing up the units of voltage and power. Volts and watts are different quantities. High voltage does not mean high power, and vice versa.
• Assuming the calculated value is available. A calculator saying R = 3,847 Ω does not mean such a resistor exists. Choose the nearest E24 value and re-check the resulting current and power.
• Forgetting to check power. A circuit that works electrically can still burn up if the power is above what the components can handle.
• Using Ohm's Law on a reactive circuit. Motors, transformers, and anything with a coil or capacitor need impedance instead of resistance.
• Ignoring the temperature coefficient. Precision circuits must account for how much a component's value changes with temperature.
• Confusing series and parallel formulas. Series adds, parallel reciprocals. Mixing them up gives wildly wrong results — remember that parallel totals are always smaller than the smallest resistor.
• Trusting the meter in-circuit for resistance. Parallel paths will always distort the reading. Disconnect one lead of the component first.
• Using peak instead of RMS for AC. If you measure 325 V peak on a mains circuit and use that as V, you will get the wrong current. Always use RMS values in Ohm's Law for resistive AC loads.
• Assuming a rated wattage is a hard maximum. Ratings are for specified conditions (usually 25 °C free air). Inside an enclosure, the effective rating is lower.

A short history of Ohm's Law

Georg Simon Ohm (1789–1854) was a German schoolteacher who spent years experimenting with the conduction of electricity through metal wires of different lengths and thicknesses. In 1827 he published his results and formulated the law that now bears his name. The reaction from the scientific establishment of his day was hostile — the leading German physicist of the time, Georg Wilhelm Friedrich Hegel, had a different philosophical view of electricity and pushed back against Ohm's experimental approach. The Prussian Minister of Education reportedly declared Ohm's work "unfruitful" and denied him a university position.

Ohm spent the next fourteen years working as a schoolteacher before the Royal Society awarded him the Copley Medal in 1841. In 1849 he finally became a professor at the University of Munich. The unit of electrical resistance, the ohm (Ω), was named in his honour by the International Electrical Congress in 1893. The symbol Ω (the Greek letter omega) was adopted because it was already in use as an abbreviation for "ohm" in electrical literature.

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Frequently asked questions

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