LED Resistor Calculator

Why an LED needs a series resistor

A light emitting diode holds its forward voltage almost constant, so the resistor in series sets the current that flows through the circuit. Give an LED exactly its forward voltage from a stiff supply and a small change in voltage moves the current a long way, which is why an LED wired straight across a battery can glow bright for a moment and then die. The resistor absorbs the voltage difference and turns the remaining volts into a predictable current.

The sizing formula follows from Ohm's law applied to the resistor alone:

• R = (Vs - Vf) ÷ I
• Vs is the supply voltage
• Vf is the LED forward voltage
• I is the current in amps

Worked example: a 5 V supply feeds a red LED with a forward voltage of 1.8 V, and the target current is 20 mA. The resistor sees 5 - 1.8 = 3.2 V, so R = 3.2 ÷ 0.020 = 160 ohms. The next standard value up is 180 ohms, which gives (5 - 1.8) ÷ 180 = 0.0178 A (17.8 mA), a little under target and safely inside the rating.

Check the voltage the other way: 20 mA through 180 ohms drops 0.020 × 180 = 3.6 V, which leaves 5 - 3.6 = 1.4 V across the LED. That is slightly below the 1.8 V forward voltage, which is why the settled current comes out below 20 mA. The LED and the resistor settle at a point where both equations agree, and the calculator reports that settled current for you.

Forward voltage depends on the LED color

The forward voltage is set by the semiconductor material, and the material sets the color, so the two travel together. The Rensselaer Polytechnic Institute circuits course notes list approximate thresholds from 1.2 V for infrared parts to 3.6 V or more for blue and ultraviolet, and the Grinnell College electronics reading puts the usual range at 1.7 V to 3.4 V for visible colors.

Those are starting points. The exact value lives in the datasheet, and it drifts with current and temperature, so a red LED specified at 2.0 V may measure 1.7 V at 5 mA. The Carnegie Mellon kinetics course exercise uses 1.6 V for a typical red part at 20 mA, which shows how much parts vary. When a datasheet is missing, start at the low end of the color's range for a dim run and measure.

Two LEDs of the same color from the same bag can differ by a tenth of a volt. That spread is invisible with a series resistor, and it is one reason the resistor design survives part swaps.

Worked examples at 3.3, 5, 9 and 12 volts

The table runs the formula for the supplies most builders keep on the bench. The exact value is (Vs - Vf) ÷ I, the standard value is the next E12 step at or above it, and the actual current and resistor power follow from that chosen resistor.

Follow the 9 V row: 9 - 1.8 = 7.2 V across the resistor, 7.2 ÷ 0.010 = 720 ohms exact, and the next E12 step up is 820 ohms, so the current is 7.2 ÷ 820 = 0.00878 A (8.78 mA). Follow the 12 V white row: 12 - 3.2 = 8.8 V, 8.8 ÷ 0.020 = 440 ohms exact, chosen 470 ohms, current 8.8 ÷ 470 = 0.0187 A (18.7 mA), and the resistor burns (0.01872)² × 470 = 0.165 W, which is inside a quarter watt rating but warm to the touch.

Notice the pattern: a higher supply with the same LED wastes more volts in the resistor. The 3.3 V red circuit gives 1.8 V to the LED and 1.5 V to the resistor, while the 12 V red circuit gives 2 V and 10 V. Both light the LED the same, but the 12 V version turns almost seven times more energy into heat per milliamp.

Rounding to a standard resistor value and which way to round

Resistors come in preferred values. The E12 series repeats twelve values per decade: 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82, then the same numbers times ten, a hundred, and so on. A computed 160 ohms does not exist in the drawer, but 150 and 180 do, and 440 ohms becomes 470.

Always round up, never down. Rounding down raises the current above target, and the margin between a typical 20 mA rating and the absolute maximum is small. Rounding up only dims the LED a few percent, which is invisible in an indicator application. The table above rounds every exact value up to the next E12 step, the twelve value series most shops stock.

Tolerance matters more than the rounding. A 5% carbon film 180 ohm resistor can measure 171 to 189 ohms, so the current in the 5 V red circuit ranges from 3.2 ÷ 171 = 0.0187 A (18.7 mA) to 3.2 ÷ 189 = 0.0169 A (16.9 mA). That spread is harmless at 20 mA ratings, and 1% metal film parts shrink it fivefold if the design sits close to the limit.

If you need a value between two steps, put two resistors in series: values in series add up, so 150 + 33 = 183 ohms. The calculator also reports the actual current for the chosen value, which is the number to compare against the datasheet maximum, not the target current you typed.

Resistor power rating and heat

The resistor turns the voltage difference into heat, and the power is P = I²R, with I in amps. A 20 mA circuit through 180 ohms burns (0.02)² × 180 = 0.072 W, comfortably inside a quarter watt part. The same 20 mA through 470 ohms burns 0.188 W, which is three quarters of a quarter watt rating and runs hot; a half watt part is the better pick there.

High current LEDs move the goalposts. A one watt LED runs at 350 mA, not 20 mA. On a 5 V supply with a 3.2 V forward voltage, the resistor is (5 - 3.2) ÷ 0.35 = 5.1 ohms, and it burns (0.35)² × 5.1 = 0.63 W, which needs a 1 W or 2 W resistor with airflow and a pad big enough to sink the heat. At that point a switching constant current driver wastes less power than a resistor does.

Rule of thumb: keep the resistor below half its rated power, and rate the part at least twice the calculated dissipation. A resistor running at its full rating reaches temperatures that discolor boards and drift in value over time.

Strings of LEDs on one supply

LEDs in series share one current, so their forward voltages add. Three white LEDs at 3.2 V each drop 9.6 V, and on a 12 V supply the resistor sees 12 - 9.6 = 2.4 V, so R = 2.4 ÷ 0.020 = 120 ohms, which happens to be an exact E12 value. Four of the same LEDs drop 12.8 V, more than the supply, and the string stays dark no matter how small the resistor gets.

Parallel strings are a different animal. Each parallel branch needs its own resistor, because two LEDs sharing one resistor do not share the current evenly: the part with the lower forward voltage hogs the current, heats up, drops less voltage, and hogs more, until it fails. That process is called thermal runaway, and one resistor for a parallel pair is the classic way to trigger it.

Series is the efficient direction: one current, one resistor, and the resistor voltage is the leftover after the LEDs. The limit is the supply, which must exceed the string total by a few volts for the resistor to do its job.

Supply tolerance and other real world errors

A 12 V automotive rail is not 12 V. With the engine running it sits near 14.4 V, and the calculator's current figure changes with it: the 12 V white circuit at 470 ohms draws 11.2 ÷ 470 = 0.0238 A (23.8 mA) at 14.4 V instead of 18.7 mA, 27% above the design point. Size the resistor for the highest voltage the rail can reach, not the nominal one, or pick a constant current driver.

Other errors worth checking before power up:

• Using 20 mA for a high power part. One watt LEDs run at 350 mA and three watt parts at 700 mA. A 20 mA calculation starves them or, if you fix the current, the resistor power is wrong.
• Ignoring the resistor tolerance direction. A minus 5% part passes more current than the math suggests.
• Sharing one resistor across parallel LEDs. Each branch gets its own resistor, as the section above explains.
• Running an LED from AC. A series diode is needed for the reverse half cycle, because most LEDs fail around 5 V of reverse voltage.
• Forgetting the datasheet maximum. Many 5 mm parts are rated 20 mA continuous and 30 mA peak, so a 25 mA design may light fine for a year and fade early.

The NIST SI unit guide covers the definitions behind the arithmetic, and a $10 multimeter covers the rest: measure the actual current through the series loop and compare it to the calculator's prediction before anything is soldered.

Checking the circuit before you solder

Breadboard first, meter second, solder third. Wire the LED and resistor in series, power it through the meter on a milliamp range, and read the loop current. The reading should sit a few percent under the calculator's prediction, because the real forward voltage will not match the assumed one exactly.

Measure the voltage across the LED itself to learn the part's true forward voltage at your chosen current, then enter that measured value back into the calculator for a second pass. One iteration is usually enough to land within 5% of any target current.

Watch the heat during the first minute. A quarter watt resistor at 0.15 W is warm but touchable, and anything that stings a fingertip after ten seconds is over its comfortable rating. Dim, correct, and re-measure; LEDs fail slowly from heat, so an overcurrent shows up as a shortened life rather than an immediate pop, which makes it easy to miss without the meter.