LED resistor formula

R = (Vs − Vf) / If

Vs - supply voltage
Vf - LED forward voltage (typically 1.8–3.5 V depending on colour)
If - desired forward current (typically 10–30 mA)

Typical LED forward voltages

Red: 1.8–2.2 V
Yellow / Orange: 2.0–2.4 V
Green: 2.0–3.5 V
Blue / White: 2.8–3.5 V

Circuit diagram

The resistor is placed in series between the power supply and the LED’s anode (positive leg):

   Vs (+)
    │
   [R] ← calculated resistor
    │
   [LED] -> anode (+) - cathode (−)
    │
   GND (−)

Current flows from Vs through the resistor, through the LED from anode to cathode, and back to ground. The resistor absorbs the “excess” voltage (Vs − Vf) and limits current to the safe If value. Without this resistor, the LED would draw uncontrolled current and burn out in milliseconds.

Nearest standard resistor values (E24 series)

Resistors are sold in standard values. After calculating R, round up to the nearest standard value to ensure current stays at or below your target (rounding down increases current). The E24 series (24 values per decade) covers all commonly available resistors: 10, 11, 12, 13, 15, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 43, 47, 51, 56, 62, 68, 75, 82, 91 … and then 100, 110, 120 … (multiply by powers of 10).

Multiple LEDs in series

When LEDs are wired in series, their forward voltages add up. Use the same formula but replace Vf with the sum of all forward voltages:

R = (Vs − ΣVf) / If

Example: 3 red LEDs in series (Vf = 2.0 V each) on a 12 V supply at 20 mA: R = (12 − 6) / 0.020 = 300 Ω. Your supply voltage must exceed the sum of all forward voltages; if Vs ≤ ΣVf, no current can flow regardless of resistor value.

PWM dimming

To dim an LED, pulse-width modulation (PWM) is strongly preferable to reducing the supply voltage or increasing the series resistance. At a lower fixed current, an LED's color temperature shifts and efficiency drops. With PWM, the LED is switched fully on and off many times per second - the duty cycle (on-time ÷ period) controls perceived brightness while the LED always operates at its rated current when on. This maintains consistent color temperature and maximizes efficiency across the full brightness range.