Ohm's Law Explained: V = I × R, Power and LED Resistor Maths

Ohm's law is the basic rule that describes the relationship between voltage (V), current (I) and resistance (R) in an electrical circuit: V = I × R. In other words, the voltage across a resistor equals the current flowing through it multiplied by its resistance. With this one-line formula you can work out which resistor an LED needs, how much current you can draw from an Arduino pin or what voltage a sensor circuit will produce, all before you burn a single part.

Almost everyone who starts with electronics asks the same first question: “Why do we put a resistor in front of an LED, and why 220 Ω?” In this article we explain Ohm's law from scratch using a water-pipe analogy. Then you'll learn, step by step, how to calculate power (P = V × I) and LED resistors, the current limits of Arduino, ESP32 and Raspberry Pi Pico pins, series and parallel resistors, multimeter measurements and how to build your own ohmmeter with an Arduino. When you don't feel like doing the maths by hand, the Ohm's law calculator and the LED resistor calculator do it in seconds.

What is Ohm's law? The V = I × R formula

In 1827 the German physicist Georg Simon Ohm showed that the current through a conductor is directly proportional to the voltage applied across it. Double the voltage and the current doubles; double the resistance and the current halves. The easiest way to remember this is the water-pipe analogy: voltage is the water pressure in the tank, current is the amount of water flowing through the pipe each second, and resistance is how narrow the pipe is. More pressure means more flow; a narrower pipe means less flow. In electricity, voltage pushes the electrons, resistance narrows their path, and current is the amount of charge that gets through.

You can use the formula in three ways. To find current, divide voltage by resistance (I = V / R); to find resistance, divide voltage by current (R = V / I); to find voltage, multiply current by resistance (V = I × R). The classic memory aid is the Ohm's law triangle: write V at the top and I and R in the bottom corners. Cover the letter you want with your finger and the two remaining letters show the operation: side by side means multiply, one above the other means divide.

Units: calculating with milliamps and kilohms

In the Arduino world, currents are usually in milliamps (mA) rather than amps, and resistances are in kilohms (kΩ) rather than ohms. 1 A = 1000 mA, 1 kΩ = 1000 Ω and 1 MΩ = 1,000,000 Ω. The most common calculation mistake is mixing up units: if you plug a 20 mA current into the formula as 20, the result is a thousand times wrong. The right way is to write the current in amps as 0.02, or to do the whole calculation consistently in mA and kΩ.

Electrical power: P = V × I

Ohm's law has an inseparable twin, the power formula: P = V × I. The power a component dissipates is the voltage across it times the current through it, measured in watts (W). Substitute Ohm's law into it and you get two more handy forms: P = I² × R and P = V² / R. The power dissipated in a resistor turns into heat, which is why every resistor has a power rating. The small carbon-film resistors you use on a breadboard are usually rated at 1/4 W (0.25 W).

For a safe design, pick a resistor rated for at least twice the power it will dissipate. A resistor too hot to touch, a darkened body or a burning smell are signs that the power limit has been exceeded. The same logic applies when choosing batteries and adapters: a project drawing 500 mA at 5 V uses 2.5 W, which is the limit of what a USB 2.0 port can supply.

LED resistor calculation step by step

An LED does not obey Ohm's law directly, because its resistance is not constant. It conducts almost no current until it reaches a certain forward voltage (Vf); once past that threshold, the current rises very quickly. If you connect an LED straight to 5 V or to an Arduino pin, nothing limits the current, and the LED, the pin or both get damaged. That's what the series resistor is for: the LED's forward voltage stays almost constant, the rest of the voltage drops across the resistor, and Ohm's law sets the current. If you're curious about how LEDs work, see What Is an LED?.

1. Find the supply voltage (Vs): 5 V on an Arduino Uno and Nano, 3.3 V on an ESP32 and Raspberry Pi Pico.
2. Find the LED's forward voltage (Vf): about 2.0 V for red, 3.0–3.2 V for blue and white. For typical values by colour, check the LED voltage table.
3. Choose the current you want (I): 20 mA is the upper limit for standard 5 mm LEDs; 5–10 mA is bright enough in most cases and doesn't strain the pin.
4. Apply the formula: R = (Vs − Vf) / I.
5. Round the result up to the next standard value (E12 series: 100, 120, 150, 180, 220, 270, 330, 390, 470 Ω…). You can find the nearest one with the standard value tool.
6. Check the power: P = (Vs − Vf) × I. For a single indicator LED the result is usually below 50 mW, so a 1/4 W resistor is fine.

Let's work through a concrete example: you're connecting a red LED to a 5 V pin on an Arduino Uno. R = (5 − 2) / 0.01 = 300 Ω, so you pick the standard value 330 Ω. The actual current is I = 3 / 330 ≈ 9.1 mA, and the resistor dissipates 3 V × 9.1 mA ≈ 27 mW. Why is 220 Ω so common in starter kits? Because with a red LED at 5 V it gives about 13.6 mA: bright and safe. Connect the same LED to a 3.3 V ESP32 pin with 330 Ω and the current drops to (3.3 − 2) / 330 ≈ 3.9 mA; the LED lights, but dimmer. On a Raspberry Pi Pico this low current is actually an advantage, because Pico pins have a default drive strength of 4 mA. The LED resistor calculator does all of this on one screen.

Arduino, ESP32 and Pico pin current limits

A microcontroller pin is a small voltage source that can only supply a limited current. When you set it HIGH it outputs 5 V or 3.3 V, but it can only hold that voltage up to a certain current. Ohm's law does the job here as well: if you know the resistance of the load on the pin, you calculate its current with I = V / R and compare the result with the pin's limit.

These limits protect the chip itself; running at the absolute maximum for long periods wears it out. The practical rule is simple: drive one or two LEDs from a pin at most and leave the rest to a transistor. For example, the coil of a classic blue 5 V relay has a resistance of about 70 Ω, so I = 5 / 70 ≈ 71 mA. That's almost twice the Uno's 40 mA limit, which is why relays are always driven through a transistor. Ready-made relay modules already carry that transistor and the protection diode on board. The same calculation applies to motors, servos, LED strips and powerful buzzers; you can choose a suitable transistor with the transistor tool.

Series and parallel resistors (in brief)

When you use more than one resistor, you reduce the circuit to a single equivalent resistance and apply Ohm's law again. In a series connection the resistors are joined end to end, the same current flows through all of them, and the total resistance is the sum of the values. In a parallel connection both ends of the resistors are shared, they all have the same voltage across them and the current splits between the branches; the total resistance is always smaller than even the smallest resistor.

The most useful application of series resistors is the voltage divider. With two resistors in series, the voltage at the middle point is Vout = Vin × R2 / (R1 + R2). This formula also comes straight from Ohm's law: a current of I = Vin / (R1 + R2) flows through the circuit, and the voltage across R2 is I × R2. For example, to bring a 5 V signal down for a 3.3 V ESP32 input, use R1 = 1 kΩ and R2 = 2 kΩ: you get 5 × 2 / 3 ≈ 3.33 V, and only 5 / 3000 ≈ 1.7 mA flows through the divider. LDR and potentiometer circuits are really voltage dividers too; see the LDR and potentiometer articles for details. The series-parallel and voltage divider tools are ready for the maths.

Pull-up resistors and Ohm's law

The 10 kΩ pull-up resistor you use when connecting a button to an Arduino is also chosen with Ohm's law. While the button is pressed, one end of the resistor is at 5 V and the other at ground, so I = 5 / 10,000 = 0.5 mA flows through it, a negligible loss even in a battery project. Fit 100 Ω instead and every press draws 50 mA while the resistor dissipates 0.25 W: the battery drains and the resistor heats up. A very large value (say 1 MΩ), on the other hand, leaves the pin open to noise. The internal resistor enabled by Arduino's INPUT_PULLUP mode is between 20 and 50 kΩ. The details of button wiring are in How to connect a button to Arduino.

Multimeter measurement examples

1. Measuring voltage: Set the multimeter to DC V and touch the probes across both ends of the component, in parallel. The circuit must be running.
2. Measuring current: Open the circuit at one point and connect the multimeter in series across the gap, with the red probe in the mA socket. All of the current must flow through the meter.
3. Measuring resistance: Switch off the circuit and disconnect at least one leg of the resistor; otherwise parallel paths will change the reading.
4. Measuring current indirectly: Measure the voltage across a resistor of known value and calculate I = V / R. It's the safest method, with no wires to unplug.

Let's go through an example: you've built a series circuit running from the 5V pin of a USB-powered Arduino through a 330 Ω resistor and a red LED to GND. With the probes across the resistor you read 2.95 V, and across the LED 1.98 V. You don't need to unplug anything to find the current: I = 2.95 / 330 ≈ 8.9 mA. The two voltages add up to 4.93 V, because USB voltage is never exactly 5.00 V; it usually sits between 4.8 and 5.1 V. The fact that the voltages in a series circuit add up to the supply is Kirchhoff's voltage law, which together with Ohm's law forms the basis of all circuit calculations.

Build your own ohmmeter with Arduino

The best way to make Ohm's law stick is to use it in code. Connect a known 10 kΩ resistor in series with a resistor of unknown value (Rx) and feed the middle point to an analog input: from the voltage it measures, the board first calculates the current (I = V / R) and then the unknown resistance (R = V / I). The wiring is as follows:

1// Gerilim bölücü ile ohmmetre / Ohmmeter with a voltage divider
2// 5V -> 10k (bilinen / known) -> A0 -> Rx -> GND
3const float VIN = 5.0;                    // besleme gerilimi / supply voltage
4const float R_KNOWN = 10000.0;            // bilinen direnç (ohm) / known resistor (ohms)
5const int ADC_PIN = A0;
6
7void setup() {
8  Serial.begin(9600);
9}
10
11void loop() {
12  int raw = analogRead(ADC_PIN);          // 0-1023
13  float vout = raw * VIN / 1023.0;        // Rx üzerindeki gerilim / voltage across Rx
14
15  if (raw >= 1020) {
16    Serial.println(F("Direnc yok / No resistor"));
17  } else if (raw <= 3) {
18    Serial.println(F("Kisa devre / Short circuit"));
19  } else {
20    float iMilli = (VIN - vout) / R_KNOWN * 1000.0;  // I = V / R (mA)
21    float rx = vout / iMilli * 1000.0;               // R = V / I (ohm)
22    float pMilli = vout * iMilli;                    // P = V x I (mW)
23    Serial.print(F("Rx = "));
24    Serial.print(rx, 0);
25    Serial.print(F(" ohm   I = "));
26    Serial.print(iMilli, 3);
27    Serial.print(F(" mA   P = "));
28    Serial.print(pMilli, 2);
29    Serial.println(F(" mW"));
30  }
31  delay(1000);
32}

The code first finds the voltage on the analog input. The current through the known resistor is the voltage across it (VIN − vout) divided by 10 kΩ; since the circuit is in series, the same current also flows through Rx. Then Rx = vout / I gives the unknown resistance, and P = V × I gives the power Rx dissipates. Because the Arduino's analog reference is the same 5 V rail, a USB voltage of 4.9 V or 5.1 V barely affects the resistance you get. The measurement is most accurate when Rx is close to the known resistor; with 10 kΩ, roughly 1 kΩ to 100 kΩ measures well.

On an ESP32 you can build the same circuit on GPIO 34; in the code set VIN = 3.3 and ADC_PIN = 34, and because the ESP32's ADC reads 0–4095, replace 1023 with 4095 (and move the "no resistor" threshold to around 4090). This ADC isn't perfectly linear, though, and can't read much above about 3.1 V, so instead of converting the raw value it's more accurate to read the voltage directly in millivolts with analogReadMilliVolts(34). The measurement is then no longer ratiometric, so set VIN to the real voltage you measure on the 3V3 pin with a multimeter. On a Raspberry Pi Pico, the same measurement in MicroPython looks like this:

1from machine import ADC
2import time
3
4VIN = 3.3                                   # Pico ADC referansı / Pico ADC reference
5R_KNOWN = 10000                             # bilinen direnç (ohm) / known resistor (ohms)
6adc = ADC(26)                               # GP26 = ADC0
7
8while True:
9    raw = adc.read_u16()                    # 0-65535
10    vout = raw * VIN / 65535                # Rx üzerindeki gerilim / voltage across Rx
11    if vout > VIN - 0.02:
12        print("Direnc yok / No resistor")
13    elif vout < 0.02:
14        print("Kisa devre / Short circuit")
15    else:
16        i_ma = (VIN - vout) / R_KNOWN * 1000    # I = V / R (mA)
17        rx = vout / i_ma * 1000                 # R = V / I (ohm)
18        print("Rx = {:.0f} ohm  I = {:.3f} mA".format(rx, i_ma))
19    time.sleep(1)

Common calculation mistakes

Projects to try Ohm's law with

• Your first LED circuit: See the brightness difference between 220 Ω and 330 Ω with your own eyes and confirm the current with a multimeter.
• Traffic light: Calculate a separate resistor for the red, yellow and green LEDs based on their forward voltages.
• RGB LED: Find out why each colour channel needs its own resistor in Using an RGB LED.
• Night light: Detect darkness with a voltage divider made of an LDR and a fixed resistor; the code is in the LDR light sensor article.
• Digital voltmeter: Safely measure voltages above 5 V with a voltage divider and show the result on an LCD.
• Pocket ohmmeter: Combine the code above with an I2C LCD display to build a portable resistance meter.

Ohm's law is the basic calculation behind every circuit you'll build, whether it's an LED, a sensor, a motor or a power supply. Once it clicks, you choose resistors by calculation instead of guesswork and never burn a part for nothing. To get to know resistors better, read What Is a Resistor?. In the BlueGrays app you'll find LED, traffic light, button, LDR and digital voltmeter projects for Arduino, ESP32 and Pico, with step-by-step circuit diagrams and code.