Resistor for a Red LED on 3.3 V: Exact and E12 Value

Ohm's law and the LED resistor, summed up by four results

Twelve volts pushing half an amp means 24 Ω of resistance and 6 W of heat. Give the calculator any two of voltage, current and resistance and it returns the third plus the power; switch to the LED mode and it sizes the series resistor from the supply voltage, the LED's forward voltage and the current you want, then rounds up to a resistor you can actually buy.

24 Ω

12 V at 0.5 A, dissipating 6 W

150 Ω

for an LED of 2 V at 20 mA on a 5 V pin

1.9149 mA

through 4.7 kΩ from a 9 V battery

1.2 kW

a 12 Ω element drawing 10 A at 120 V

Setting up a calculation

What to calculate - resistance, voltage, current, or the series resistor for an LED.
Voltage and its unit - mV, V or kV. In LED mode this is the supply: a 5 V USB rail, a 9 V battery, a 12 V car socket.
Current and its unit - µA, mA or A. Type 500 with mA selected rather than 0.5 with A if that is how the number is printed.
Resistance and its unit - Ω, kΩ or MΩ. A resistor marked 4k7 is 4.7 with kΩ selected.
LED forward voltage - LED mode only, in volts, from the datasheet.
Read the result - the answer with a sensible prefix, the formula with your numbers, all four quantities, and in LED mode the next standard resistor values with the current each one gives.

Enter sizes without a sign. The direction a current flows in does not change the arithmetic, and a negative resistance has no meaning for a resistor.

The relationship behind every mode

Ohm's law is one sentence: the current through a conductor equals the voltage across it divided by its resistance. Written three ways it becomes I = V ÷ R, V = I × R and R = V ÷ I, which is why knowing any two numbers is enough. Voltage is the push, measured in volts; current is the flow, in amperes; resistance is how hard the component makes that flow, in ohms. One volt across one ohm drives exactly one ampere.

Power comes along for free. Multiply voltage by current and you get watts, the rate at which the resistance turns electrical energy into heat. That heat is the whole point in a toaster and a nuisance in a circuit board, where a resistor rated for a quarter of a watt will run hot or fail if it has to shed more. The calculator prints the power in every mode so you can check the rating before you solder anything.

An LED does not behave like a resistor. Its voltage stays close to the forward voltage printed in the datasheet while the current can swing a long way, so connecting it straight to a supply lets the current run away. A resistor in series takes up the difference between the supply and the forward voltage, and Ohm's law sizes it: R = (Vs − Vf) ÷ I. With a 5 V supply, a 2 V LED and a 20 mA target, the resistor sees 3 V and needs 150 Ω.

Resistance itself depends on the material and the shape. A wire's resistance is its resistivity times its length, divided by its cross-section. Resistivity is the property of the material alone, and it spans an enormous range, from silver and copper to plastics that barely conduct at all.

Doing the arithmetic on paper, prefixes included

Most mistakes with Ohm's law are not in the formula but in the prefixes. Three habits keep them out.

Milliamps times kilohms gives volts. The thousandth and the thousand cancel, so 2.5 mA through 4.7 kΩ is simply 2.5 × 4.7 = 11.75 V, with 29.375 mW of heat. In the other direction, volts divided by kilohms gives milliamps: 12 V across 2.2 kΩ is 12 ÷ 2.2 = 5.4545 mA, and the resistor dissipates 65.455 mW. Mix amps with kilohms and the answer comes out a thousand times off.

Round an LED resistor up within its decade. A 2.9 V LED at 15 mA on 5 V needs (5 − 2.9) ÷ 0.015 = 140 Ω. Divide by the decade to get 1.4, find the next number up in the series (1.5 in both E12 and E24), and multiply back: 150 Ω. That leaves the LED at 14 mA.

A wire's resistance counts both conductors. Copper at 1.68 × 10⁻⁸ Ω·m, 10 m long and 1.5 mm² across, has 1.68 × 10⁻⁸ × 10 ÷ (1.5 × 10⁻⁶) = 0.112 Ω. Current goes out and comes back, so a two-wire run of that length is 0.224 Ω. At 10 A that loses 2.24 V and warms the cable with 22.4 W, a figure you can check in voltage mode.

Resistivity of common metals at 20 °C

Values from the resistivity table on Wikipedia. The last column is the resistance of a piece 1 m long with a 1 mm² cross-section, a round size that makes the comparison concrete.

Material	Resistivity (Ω·m)	1 m × 1 mm²	Where it shows up
Silver	1.59 × 10⁻⁸	15.9 mΩ	Exposed contact points
Copper	1.68 × 10⁻⁸	16.8 mΩ	Building wiring, cables
Annealed copper	1.72 × 10⁻⁸	17.2 mΩ	The 100% IACS reference
Gold	2.44 × 10⁻⁸	24.4 mΩ	Electrical contacts
Aluminum	2.82 × 10⁻⁸	28.2 mΩ	Overhead power lines
Tungsten	5.60 × 10⁻⁸	56 mΩ	Lamp filaments
Iron	9.70 × 10⁻⁸	97 mΩ	Structural, magnetic cores
Lead	22.0 × 10⁻⁸	220 mΩ	Battery plates
Stainless steel (18/8)	69.0 × 10⁻⁸	690 mΩ	Hardware, housings
Nichrome	110 × 10⁻⁸	1.1 Ω	Heating elements

The spread explains the choice of materials. Nichrome resists about 65 times as much as copper for the same size, which is exactly what a heating element wants and exactly what a supply cable does not.

Typical LED values and what they give

Forward voltage depends on the color. Wikipedia's LED circuit article gives about 1.7 to 2.0 V for red, about 2.8 to 4.0 V for violet and around 1.2 V for infrared, and lists 2 mA, 10 mA and 20 mA as common indicator currents. The rows below are calculator results; always take the real forward voltage and maximum current from your part's datasheet.

Supply	Forward voltage	Target current	Exact resistor	Next E12 value
3.3 V	1.8 V	10 mA	150 Ω	150 Ω
5 V	2 V	2 mA	1.5 kΩ	1.5 kΩ
5 V	2 V	20 mA	150 Ω	150 Ω
9 V	2 V	20 mA	350 Ω	390 Ω
12 V	3.2 V	20 mA	440 Ω	470 Ω

Did you know?

Silver barely beats copper. Its resistivity is 1.59 × 10⁻⁸ against copper's 1.68 × 10⁻⁸ Ω·m, and making a copper wire about 3% thicker closes the gap. Silver earns its place on contacts because tarnished silver still conducts, while corroded copper does not.

Power lines are aluminum for a reason that is not resistance. Aluminum resists 2.82 × 10⁻⁸ Ω·m, more than copper, but it is far lighter for the same conductance, and weight is what matters on a long span between towers.

A resistor's value is only a promise within a band. Parts from the E12 series come with a 10% tolerance and E24 parts with 5%, which is why the E24 list has twice as many steps per decade: 24 against 12.

Metals resist more when they are hot. Copper's resistivity rises by about 0.4% per degree Celsius (temperature coefficient 4.04 × 10⁻³ per kelvin), so a heating element or a lamp filament measured cold with a meter reads lower than its working resistance.

Half the power in a simple LED circuit can be heat. On a 5 V supply at 20 mA, a 2 V LED uses 40 mW and its resistor burns 60 mW of the 100 mW drawn.

Five people with a V, an I and an R

A student checking homework. 1 mA through 1 kΩ gives 1 V and 1 mW, the textbook case where every number is one, useful for spotting a slipped prefix.

A maker wiring an Arduino. A 10 kΩ pull-up on a 5 V pin carries 500 µA and wastes 2.5 mW; an LED on a 3.3 V board with a 1.8 V forward voltage at 10 mA needs 150 Ω.

Someone looking at an appliance label. A heater drawing 10 A from 120 V works out at 12 Ω and 1.2 kW; a 240 Ω load on the same outlet takes 500 mA and 60 W.

A driver adding a light to a car. A 21 W bulb drawing 1.75 A on 12 V behaves like 6.8571 Ω while it is lit. A 3.2 V LED on the same 12 V at 20 mA needs 440 Ω; the next E24 value, 470 Ω, gives 18.723 mA and turns 164.77 mW into heat, more than a 1/8 W part should carry.

A phone charger question. 2 A through an effective 2.5 Ω load is 5 V and 10 W.

Short answers about volts, amps and ohms

Why round the LED resistor up and not to the nearest value?

A larger resistor means less current, and less current is the safe side. For a 9 V supply, a 2 V LED and 20 mA the exact value is 350 Ω; the next E24 value, 360 Ω, gives 19.444 mA and the next E12 value, 390 Ω, gives 17.949 mA. The LED looks practically the same.

What happens if the supply is lower than the forward voltage?

Nothing useful. There is no voltage left for a resistor, and the LED will not light properly. The calculator refuses the case instead of printing a negative resistance.

How do I read 4k7 or 2R2 on a schematic?

The letter stands in for the decimal point and gives the prefix: 4k7 is 4.7 kΩ, 2R2 is 2.2 Ω. Type the number and choose the prefix in the unit box.

Does Ohm's law work for a light bulb?

At one operating point, yes: a 21 W bulb at 12 V and 1.75 A is 6.8571 Ω while lit. The filament's resistance rises as it heats, though, so a meter on a cold bulb reads less, and the voltage-current line is not straight across the whole range.

What power rating does my resistor need?

More than the power the result shows. 60 mW in a 5 V LED circuit sits comfortably under a 1/4 W part; 164.77 mW on a 12 V supply already exceeds 1/8 W. Leaving some margin keeps the part cooler.

Can I use it for AC outlets?

For resistive loads such as heaters and incandescent lamps, the usual RMS voltage and current work in the same formulas, as in the 120 V heater example. Motors, transformers and electronic power supplies add reactance and power factor, which this calculator does not model.

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What resistor does a red LED need on 3.3 V?

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