A voltage divider is two resistors in series across a supply, with the output taken from the point between them. It produces an output that is a fixed fraction of the input, and it appears everywhere: setting reference voltages, scaling a signal to fit an ADC, biasing a transistor, or reading a sensor.
The divider equation
With R1 on top (connected to the input) and R2 on the bottom (connected to ground), the output is taken across R2:
Vout = Vin × R2 / (R1 + R2)
The two resistors carry the same current because they are in series, and each drops a share of the supply in proportion to its value. The output is simply R2's share.
A worked example
Take Vin = 12 V with R1 = R2 = 10 kΩ. Because the resistors are equal, the output is exactly half the input:
Vout = 12 V × 10k / (10k + 10k) = 6 V
The current through the chain is Vin / (R1 + R2) = 12 V / 20 kΩ = 600 µA. Want 3 V out instead? Make R2 one third of the total — for example R1 = 20 kΩ and R2 = 10 kΩ gives 12 × 10k/30k = 4 V; for 3 V use R1 = 30 kΩ, R2 = 10 kΩ.
Loading effects — the catch
The clean equation above assumes nothing draws current from the output. The moment you connect a load resistance RL across R2, that load is in parallel with R2 and pulls the output down:
R2_eff = (R2 × RL) / (R2 + RL)
If the load is much larger than R2 (say 100× or more), the sag is negligible. If it is comparable, the output can drop dramatically.
- Pick divider resistors small enough that the load barely perturbs them — a common rule is RL ≥ 10 × R2.
- But not so small that the divider wastes current and heats up: there is a trade-off between stiffness and power.
- For a signal that must drive a real load, buffer the divider output with an op-amp follower instead of loading it directly.