Voltage divider formula
A voltage divider (resistive divider) is two resistors in series: the input voltage is shared between them in proportion to their values, and the midpoint gives you a lower voltage. It is the simplest way to scale a voltage down so a microcontroller can read it, or to bias a transistor.
The same current I = Vin / (R₁ + R₂) flows through both resistors, so the voltage across R₂ is:
Vout = Vin · R₂ / (R₁ + R₂)
Example · 12 V with R₁ = 10 kΩ and R₂ = 4.7 kΩ
Vout = 12 · 4.7 / (10 + 4.7) = 12 · 0.3197 ≈ 3.84 V. The current is 12 / 14.7 kΩ ≈ 0.82 mA.
The loading effect
The formula above only holds if no current is drawn from the output. When you connect a load RL, it ends up in parallel with R₂ and the voltage drops: replace R₂ with R₂ ‖ RL = R₂·RL / (R₂ + RL). Seen from the load, the divider is a Vout source with an internal resistance Rth = R₁ ‖ R₂ (its Thévenin equivalent).
Example · the same divider with a 10 kΩ load
R₂ ‖ RL = 4.7 · 10 / 14.7 ≈ 3.20 kΩ, and Vout = 12 · 3.20 / 13.20 ≈ 2.91 V: almost 24% less than with no load.
That is why dividers are used for voltage references, ADC inputs and logic level shifting, but not to power circuits that draw current: that is a job for a voltage regulator.
How to design a voltage divider
- Compute the ratio R₂ / (R₁ + R₂) = Vout / Vin.
- Pick R₂ based on the current you can afford and the load it will drive (1 kΩ to 100 kΩ is typical).
- Solve R₁ = R₂ · (Vin − Vout) / Vout and find the nearest standard value.
The "Design a divider" tab tries every E12 or E24 combination and ranks the closest ones. For example, to go from 5 V to 3.3 V, the common 1.8 kΩ / 3.3 kΩ pair gives 3.24 V (2% low), while 4.7 kΩ / 9.1 kΩ gives 3.297 V, under 0.1% off.
Frequently asked questions
Can I use a divider to step 12 V down to 5 V to power an Arduino?
No. The Arduino's current draw acts as a varying load and the voltage would change with it. Use a linear regulator (such as a 7805) or a switching regulator.
Which resistor values should I choose?
Low values waste more current but hold the voltage better under load; high values draw little current but are more sensitive to noise and to the input impedance of whatever you connect. For microcontroller inputs, 10 kΩ – 100 kΩ usually works well.
How much power do the resistors dissipate?
Each one dissipates I² · R. With kilohm values and a few volts it is milliwatts, but check it with the Ohm's law calculator if you work with higher voltages.