Calculating The Minimum Resistor Value For An LED

Have you ever wondered why we typically see 330 Ω resistors used when interfacing light emitting diodes (LEDs) to digital electronics? Let’s figure out why that is.

Why does the minimum resistor size matter? Because if the resistance is too small, we could damage the LED, or worse, the surrounding circuitry. This would cause us to either waste time troubleshooting why something is not working quite right, or worse, cause a little smoke cloud on our workbench forcing us to purchase new components or entire development boards.

First, we need to understand the electrical environment where the resistor will be used. This involves knowing the maximum and minimum values for the various voltages, currents, etc. that the resistor will encounter.

Digital electronics typically have supply voltages, V_s, that fall within the 4.5 to 5.5 V range.

The forward voltage, V_f, of an LED often falls somewhere between 1.2 V and 4.0 V depending on the type of LED.

Again, depending on the type of LED, the maximum recommended forward current, I_f, typically has a range of 15-80 mA.

And finally, resistor tolerances, T_r, typically range between 1% and 10%. This means that a resistor with a specified value of 330 Ω and tolerance of 10% can actually have a resistance as low as 297 Ω (330 – 10%) or as high as 363 (330 + 10%) Ω.

To summarize:

• Supply Voltage: V_s = 5 ± 0.5 V
• LED Forward Voltage: V_f = 1.2-4.0 V
• Maximum Recommended LED Forward Current: I_f = 15-80 mA
• Resistor Tolerance: T_r = 1-10%

To calculate the resistance value needed for a resistor placed in series with an LED, we will use Ohms Law

\(\large V=IR\)

which can be rewritten as

\(\large R=\frac{V}{I}\)

and entering the voltage across the resistor and the current through the resistor for the V and I values respectively.

To determine the minimum resistance value required, we need to know the largest possible voltage drop across the resistor along with the smallest maximum current through the resistor. In addition, we want to account for the smallest resistance value possible based on its tolerance specification. Taking all these into account, the previous equation becomes

\(\large R=\frac{V_{s(max)}-V_{f(min)}}{I_{f(min)}(1-T_{r(max)})}\)

Entering actual values into the equation, we get

\(\large R=\frac{5.5-1.2}{0.015(1-0.1)}\approx318.5\hspace{0.25em}\Omega\)

Since this is not a standard resistor size, we want to round up to the next highest standard value, which gives you 330 Ω.

This is the smallest resistor value that can safely be used with almost all LEDs without damaging the LED or the digital circuitry to which it is connected. The resistor value, however, may need to be lower to sufficiently supply power to some of the more exotic types of LEDs. Additionally, you may want a smaller resistor value in order to have a brighter LED, but be careful as many digital electronics have a maximum current of 20 mA.

Let’s see a couple of real world examples:

For a Standard Red 5mm LED:

\(\large R=\frac{5.5-1.7}{0.018(1-0.1)}\approx234.6\hspace{0.25em}(240)\hspace{0.25em}\Omega\)

For a Super Bright White 10mm LED:

\(\large R=\frac{5.5-3.0}{0.07(1-0.1)}\approx39.7\hspace{0.25em}(43)\hspace{0.25em}\Omega\)

These values are for specific LEDs and may be too small for some LEDs. Also, note that the super bright white LED requires a current much larger than the 20mA maximum current mentioned earlier.

Hence, this is why we typically see 330 Ω resistors used when interfacing LEDs across a wide variety of circuits.

As always, please consult the datasheets for the components used in your particular application to determine the best resistor values needed in your circuit.