Setting an LED's current-limiting resistor with variation included

Vf is a "typical" figure, and it varies between parts

Datasheet Vf applies at a stated current and temperature. The calculations here assume 2.8–3.4V for a white LED; that interval is an example, not a guaranteed range for a particular part. Use the selected part's limits and temperature/current curves, and do not treat typical values as guaranteed bounds.

Design with the minimum Vf for the condition that maximizes current, and the maximum Vf for the condition that minimizes it.

How far current moves under worst-case conditions

A white LED (Vf typical 3.0V, range 2.8–3.4V) at 10mA from 5V gives R = (5 − 3.0) / 0.01 = 200Ω. With ±5% on the supply and ±1% on the resistor, current peaks at high supply, low Vf, low resistance: (5.25 − 2.8) / 198 = 12.4mA, and bottoms out at the opposite: (4.75 − 3.4) / 202 = 6.7mA. Against a 10mA target the range is 6.7–12.4mA, roughly a factor of two.

With 3.3V ±3% and 30Ω ±1%, the estimated maximum is (3.399 − 2.8) / 29.7 ≈ 20.2mA. At the other corner, 3.201V is below the assumed 3.4V Vf. The fixed-Vf model returns zero, but it cannot predict the real LED's small nonlinear current or visible brightness.

Less voltage headroom makes Vf variation more significant. For an explicit current requirement, calculate the admissible resistor interval below.

Find the nominal-resistor interval from the required current

With resistor tolerance t, allowable maximum current Imax and required minimum current Imin, nominal R must satisfy R ≥ (Vsmax − Vfmin) / [Imax(1 − t)] and R ≤ (Vsmin − Vfmax) / [Imin(1 + t)]. These inequalities use the fixed-Vf approximation and require positive voltage headroom.

For 5V ±5%, Vf = 2.8–3.4V, ±1% resistance and a required 7–12mA, the lower bound is 206.2Ω and the upper bound 191.0Ω: no overlap. Changing 200Ω to 220Ω cannot satisfy both. Relaxing the requirement to 6–12mA gives an upper bound of 222.8Ω; 220Ω then yields about 6.08–11.25mA. That is a candidate within these assumptions; brightness and temperature behaviour still need checking.

Size the resistor's power rating from the maximum current

Dissipation is I²R: 0.01² × 200 = 20mW at 10mA, but 0.0124² × 198 = 30mW at the maximum 12.4mA. Rate the resistor against that maximum.

Package size alone does not determine the rating. For example, Vishay D/CRCW e3 specifies 0.063W for 0402 and 0.10W for 0603 in its standard operating mode; other modes and series differ. Check the selected resistor's derating curve, mounting conditions and working-voltage limit.

If you choose a 50% loading target for the 30mW example, the required rating is at least 60mW. That margin is a design choice here, not a universal standard requirement. Compare against the allowable power after temperature derating.

Do not let several LEDs share one resistor

Two LEDs in parallel on one resistor push current toward the one with the lower Vf. With Vf of 2.9V and 3.1V, the 0.2V difference means several times the current: one LED lights brightly, the other barely. As it warms, its Vf drops further and pulls in more current. For parallel LEDs use one resistor per LED.

Series LEDs share current: R = (Vcc − ΣVf) / I. Four red LEDs assumed at 2.0V each leave 4V nominal headroom from 12V. Check the sums of maximum and minimum Vf with supply tolerance using the same current-limit inequalities as for one LED.

• Driving from a GPIO. Its tens of ohms of output resistance pull the output below the rail. Recalculate with the VOH spec (e.g. 2.4V on 3.3V) and check the port's total current limit.
• PWM dimming. On-state voltage and resistance determine instantaneous current. Check the LED's pulse-current, pulse-width and duty limits, and the resistor's pulse capability as well as average power.
• Reverse voltage. Check the selected LED's reverse-voltage rating; some parts are not intended for reverse operation. Do not assume 5V is safe. Consider protection if polarity can reverse.

What the calculator handles

The LED drive circuit calculator implements this math. Enter the maximum and minimum of supply, Vf and resistor tolerance, and it returns the current range, the worst-case dissipation and the rating needed. If the spread exceeds a factor of two, raise the supply or consider constant-current drive.