Calculator of Alexandria

Voltage divider calculator

Find the output voltage of a two-resistor voltage divider, or the resistor value you need for a target voltage.

Solve for

Formula

Vout=VinR2R1+R2V_{out} = V_{in} \frac{R_2}{R_1 + R_2}
How it's derived

The formula

Vout=Vin⋅R2R1+R2V_{out} = V_{in} \cdot \frac{R_2}{R_1 + R_2}

R1R_1 connects the input to the output, R2R_2 connects the output to ground, and VoutV_{out} is measured across R2R_2.

Where it comes from

With nothing connected to the output, the same current II flows through both resistors, because there’s nowhere else for it to go. In series their resistances add, so by Ohm’s law

I=VinR1+R2I = \frac{V_{in}}{R_1 + R_2}

The output voltage is the voltage across R2R_2, which by Ohm’s law again is

Vout=IR2=VinR1+R2⋅R2V_{out} = I R_2 = \frac{V_{in}}{R_1 + R_2} \cdot R_2

The input voltage is shared between the two resistors in proportion to their resistance. Solving for R1R_1 when you know the voltages you want:

R1=R2⋅Vin−VoutVoutR_1 = R_2 \cdot \frac{V_{in} - V_{out}}{V_{out}}

Worked example

Scaling 5 V down to a 3.3 V logic level with R2=20R_2 = 20 kΩ:

R1=20 kΩ×5−3.33.3=10.3 kΩR_1 = 20\ \text{k}\Omega \times \frac{5 - 3.3}{3.3} = 10.3\ \text{k}\Omega

so a standard 10 kΩ resistor gives 5×20/30=3.335 \times 20/30 = 3.33 V.

Watch out for

  • Loads change the answer. Anything connected to the output draws current in parallel with R2R_2, lowering VoutV_{out}. Keep the load resistance at least ten times R2R_2, or buffer the output.
  • Don’t power things from a divider. It wastes current through the resistors and sags under load; use a regulator instead.

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