Electronics

# Calculating The Minimum Resistor Value For An LED

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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, Vs, that fall within the 4.5 to 5.5 V range.

The forward voltage, Vf, 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, If, typically has a range of 15-80 mA.

And finally, resistor tolerances, Tr, 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: Vs = 5 ± 0.5 V
• LED Forward Voltage: Vf = 1.2-4.0 V
• Maximum Recommended LED Forward Current: If = 15-80 mA
• Resistor Tolerance: Tr = 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.

### About the author

#### John Woolsey

John is an electrical engineer who loves science, math, and technology and teaching it to others even more.

He knew he wanted to work with electronics from an early age, building his first robot when he was in 8th grade. His first computer was a Timex/Sinclair 2068 followed by the Tandy 1000 TL (aka really old stuff).

He put himself through college (The University of Texas at Austin) by working at Motorola where he worked for many years afterward in the Semiconductor Products Sector in Research and Development.

John started developing mobile app software in 2010 for himself and for other companies. He has also taught programming to kids for summer school and enjoyed years of judging kids science projects at the Austin Energy Regional Science Festival.

Electronics, software, and teaching all culminate in his new venture to learn, make, and teach others via the Woolsey Workshop website.

• Mike Collins says:

Clear, crisp, concise explanation. Well done John!

• What is forward voltage, I have never heard an explanation that will stick with me.

• Forward voltage is the voltage drop across a diode when its anode (positive terminal) is at a higher voltage than its cathode (negative terminal). A diode connected in this way is referred to as being forward biased. A diode connected in the opposite direction has a reverse voltage and is reverse biased. LEDs only “turn on” when they are forward biased which is why you typically see specifications for Vf and If.

• Oh. I guess I always assumed that the negative part had a zero voltage. Is forward voltage just another way of saying positive end of, in this case the LED?

• It is not really the “end” of something as much as across something. Typically you put a resistor in series with an LED to limit the current through the LED. The resistor could be connected from the positive terminal of a battery to the positive terminal (anode) of the LED or the resistor could be connected from the negative terminal (cathode) of the LED to ground. So the forward voltage is the difference in the voltage across the LED regardless of how it is connected.

• Put another way, is it safe to say the voltage after the diode is lower than prior to the diode? Sorry for all these dumb questions but it isn’t like that many people know this stuff!

Also, does a resistor thought to block amps, volts or both? I’ve never known that either.

• No problem. Glad I can help. That is correct. A resistor resists (limits) the flow of current (amps). Sound like you got it.

• Instead of forward voltage why not call it soaked up voltage?

Just so I understand, is it ok to say v5-forward voltage number=output voltage?

Thanks again, I don’t know if I have trouble with these concepts because of the words used or for some other reason. Often if the words used don’t match my understanding of those words I can’t quite get the concept. I just realized that now of all things and I am close to social security age!

• Forward voltage is not referring to whether the device produces or consumes, but whether the device is connected in a forward or reverse orientation. The device could still have a voltage drop in both orientations.

Forward voltage is not equivalent to output voltage. Output voltage is used for devices that produce or supply a voltage, such as a battery or AC/DC converter/adapter.

• Mitch says:

Hi tnx for the explanation…I’m wondering if my understanding is correct…from my bread board experiment with 4 different coloured LEDs wired up in parallel, each attached to a 330 Ohm resistor, and from my calculations from analyzing the circuit, I found that the same value of resistors can incur different voltage drops…this leads me to believe that a resistor basically soaks up whatever voltage is necessary in order for the circuit to find it’s equilibrium…if this is true, you could plunk in resistors with higher Ohms ratings than calculated with no effect since the resistor would only absorb enough voltage to balance the circuit…so my question is, do resistors have a lower limit whereby if not enough voltage is applied, the resistor won’t allow any current to flow through at all? Or, if not, could you use a 10K Ohm resistor to handle a job that only required a 100 Ohm resistor for example? Sorry for the long question…tnx again.

• Nice to see you are doing your own experiments!
Your understanding is close, but not quite correct. A resistor limits the current in a circuit. It will automatically adjust the voltage across the resistor based on the current flowing through the resistor according to Ohm’s Law V = I*R. I believe you are seeing the voltage differences because you are using different LED colors. Each color of an LED produces a different voltage drop across the LED. In addition, even if you used the same resistor values with the same LED colors, the voltages would still be slightly different due to slight differences during the manufacturing process. Let’s say a particular LED has a voltage drop of 2V when connected to a 330 ohm resistor and 5V power. The resistor will assume the voltage that is the difference between the voltage drop of the LED and the voltage supply. In this case, that would be 5 – 2 = 3V. This is similar to what you were thinking, but you need to take into account the current differences as well. LED’s have a limited range of allowable current values that will light the LED, so while resistors with different values may have similar voltages when used with the LED, the currents will be widely different.

So to answer your question, a 10K resistor would not provide enough current to drive the LED. Try using a 500 ohm, or even a 1K ohm, resistor and you should see the light intensity of the LED drastically reduced.

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