LED Resistor Equation
LEDs are current-driven devices. A series resistor is used to drop the excess voltage from the power supply while passing the specific current the LED requires.
Where:
- Vs = Power supply voltage
- Vf = LED forward voltage drop (e.g., 2V for red, 3.3V for blue)
- If = Forward current (usually 10mA to 20mA for standard LEDs)
Frequently Asked Questions
Subtract the LED forward voltage from the power supply voltage, then divide that result by the desired current (in Amperes). Formula: R = (Vs - Vf) / I.
An LED (Light Emitting Diode) has a very low forward voltage (Vf = 1.8–3.5V depending on colour) and minimal internal resistance — it cannot self-limit current. Without a series resistor, the LED draws unlimited current until it destroys itself. The resistor limits current to the safe operating range, typically 10–20mA for standard 5mm and 3mm LEDs, and 350mA–3A for high-power LEDs.
LED resistor formula: R = (Vs − Vf) / If. Where R = resistor value (Ω), Vs = supply voltage (V), Vf = LED forward voltage (V), If = desired forward current (A). Example: 12V supply, white LED (Vf = 3.2V), 20mA: R = (12 − 3.2) / 0.020 = 440Ω. Select nearest standard resistor value (in this case 470Ω, giving 18.7mA — slightly lower, which is fine).
Typical LED forward voltages (Vf) at 20mA: Infrared — 1.2–1.7V; Red — 1.8–2.2V; Orange/Amber — 2.0–2.2V; Yellow — 2.0–2.4V; Green (standard, GaP) — 2.0–2.4V; Green (high-brightness, InGaN) — 3.0–3.5V; Blue — 3.0–3.5V; White (blue chip + phosphor) — 3.0–3.5V; UV — 3.5–4.2V. Always confirm with the specific LED's datasheet.
For series LEDs: All share the same current. Calculate: R = (Vs − n × Vf) / If, where n is the number of LEDs. Example: 12V supply, 3× red LEDs (Vf=2.0V each), 20mA: R = (12 − 3×2.0) / 0.020 = (12−6)/0.020 = 300Ω. Series wiring is efficient but if one LED fails open-circuit, all go dark. Never share a single resistor across parallel LEDs — slight Vf differences cause unequal currents.
Calculate resistor power: P = (Vs − Vf)² / R, or P = If² × R. Example: 470Ω resistor with 18.7mA: P = 0.0187² × 470 = 0.164W. Use a resistor rated at 2× calculated power for safety — so use a 1/4W (0.25W) or 1/2W resistor. Standard ratings: 1/8W, 1/4W, 1/2W, 1W, 2W, 5W. For high-power LED arrays (hundreds of mA), use a dedicated LED driver IC rather than resistors.
LED Current-Limiting Resistors: Why and How
An LED is a non-linear device: above its forward-voltage threshold (VF), the current it draws rises almost vertically with applied voltage. Connecting an LED directly across a battery or power supply — even one whose voltage looks “close enough” to VF — almost always destroys the LED within seconds, because tiny voltage variations translate into massive current swings. The current-limiting resistor in series with the LED solves this by absorbing the voltage difference between the supply and the LED’s drop, forcing the current to a safe steady-state value defined by Ohm’s law on the resistor itself.
The Calculation
Three knowns drive the answer: VS (supply voltage), VF (LED forward voltage at the design current), and IF (design forward current, typically 10–20 mA for indicator LEDs). The required series resistance is R = (VS − VF) / IF. The power dissipated in the resistor is PR = (VS − VF)² / R = (VS − VF) × IF, which determines the resistor’s required wattage rating — choose at least 2× this value to keep the resistor running cool. Common LED VF values: red ~1.8–2.1 V, yellow/orange ~2.0–2.2 V, green ~2.0–3.5 V (depending on chemistry), blue/white ~3.0–3.5 V, UV ~3.5–4.0 V.
Worked Example: A Red LED on 5 V Logic
You want to drive a standard 5 mm red LED (VF = 2.0 V at 20 mA) from a 5 V Arduino output. R = (5 − 2.0) / 0.020 = 150 Ω. Power in the resistor = 3.0 V × 0.020 A = 0.060 W = 60 mW — a standard 1/4 W (250 mW) resistor is way more than enough. Pick the nearest E12 standard value (150 Ω happens to be exact, otherwise round up to the next standard). For a brighter LED at 25 mA: R = 3 / 0.025 = 120 Ω, P = 75 mW — still fine on 1/4 W. Run the LED resistor calculator above with these inputs and you get the same answer in one click, plus colour-band suggestions.
Driving Multiple LEDs — Series vs Parallel
Series chain of LEDs share the same current automatically, but the VF values add up: 4 white LEDs at 3.2 V each need VS > 12.8 V plus headroom for the resistor — not feasible from 5 V. Parallel arrangement of LEDs on a single resistor is unreliable: small VF mismatches between LEDs cause one to hog the current and burn out, then the next, in cascade. The correct approach for multiple LEDs is one resistor per LED (or one resistor per series chain), even if it costs a few extra parts. The calculator handles series-chain calculation if you sum the VF values manually before entering.
PWM Dimming and Constant-Current Drivers
For brightness control, PWM (pulse-width modulation) is preferred over reducing forward current via a larger resistor: PWM keeps the LED at its rated current during ON pulses, which preserves the colour temperature and efficiency. For high-power LEDs (1 W and above), abandon the resistor approach entirely and use a constant-current LED driver IC (LM317-based, or dedicated chips such as PT4115 or MEAN WELL constant-current modules) — these maintain current within ±5% across supply-voltage and temperature variations, and they don’t waste energy as resistor heat.
Related calculators: Ohm’s Law · Resistor color code · 555 timer · Voltage divider · All electrical calculators