Solve a two-resistor voltage divider for output, input, or either resistor, including load resistance, divider current, power, loading error, and tolerance range.

Steady DC divider: Rtop connects input to output; Rbottom and the optional load connect output to ground. Uses an ideal source and positive linear resistances. This is not a regulated power supply or a component rating check.

Load and resistor limits

Blank means no load. A load connects in parallel with Rbottom.

Optional independent limits on Rtop and Rbottom. Blank or 0 omits the range; input voltage and load stay fixed.

Output Voltage Formula

In a two-resistor voltage divider, the output appears across R1, the bottom resistor from output to ground. In the widget this is Rbottom; article R2 is Rtop, from input to output. The formulas below use this article naming.

Vₒ = Vᵢ × (R₁) / (R₁ + R₂)
  • Vo = output voltage across R1
  • Vi = input voltage supplied to the divider
  • R1 = resistor across which the output is measured
  • R2 = the other series resistor in the divider

The equation shows that output voltage depends on the ratio of the resistors, not just their individual values. As R1 becomes a larger share of the total resistance, the output voltage increases. As R2 becomes larger relative to R1, the output voltage decreases.

How to Calculate Output Voltage

  1. Enter the input voltage.
  2. Enter the values for R1 and R2 using the same resistance unit.
  3. Add the two resistances to get the total series resistance.
  4. Divide R1 by the total resistance to find the divider ratio.
  5. Multiply that ratio by the input voltage.
(Vₒ) / (Vᵢ) = (R₁) / (R₁ + R₂)

This ratio makes quick estimation easy. If R1 is one-half of the total resistance, the output is one-half of the input. If R1 is one-fourth of the total resistance, the output is one-fourth of the input.

Rearranged Forms

If you know any three values, the relationship can be rearranged to solve for the missing one.

Solve for Input Voltage

Vᵢ = Vₒ × (R₁ + R₂) / (R₁)

Solve for R1

R₁ = (Vₒ R₂) / (Vᵢ - Vₒ)

Solve for R2

R₂ = R₁ × (Vᵢ - Vₒ) / (Vₒ)

For positive input voltage and positive resistors, output across R1 lies between zero and the input. For negative input, output has the same polarity and smaller magnitude. Solving a resistor requires a nonzero voltage ratio strictly between 0 and 1; zero input and output cannot determine resistance.

Example

If the input voltage is 12 V, R1 is 3 kΩ, and R2 is 9 kΩ, the output voltage across R1 is:

Vₒ = 12 × (3) / (3 + 9) = 3 V

If the two resistors are equal, the output is exactly half of the input:

Vₒ = Vᵢ × (R₁) / (R₁ + R₁) = (Vᵢ) / (2)

Practical Notes

  • Keep resistance units consistent: Hand calculations must use a common unit. The widget converts the selected voltage and resistance units, including when a unit is changed.
  • The output cannot exceed the input in a passive divider: a divider reduces voltage; it does not amplify it.
  • Component tolerance matters: Enter an optional common ±% limit to vary the two divider resistors independently at their worst-case corners, while input voltage and load resistance stay fixed. Blank or zero omits this range; actual components are not assumed exact.
  • Very small resistor values draw more current: the voltage ratio may be correct, but power loss and heating increase as total resistance decreases.
  • Very large resistor values reduce current draw: this is often useful, but extremely high values can make the circuit more sensitive to leakage and loading.

Loaded Divider Adjustment

The basic formula assumes the output is not significantly loaded by another component. If a load resistor is connected across the output, first combine it with R1 as a parallel equivalent, then use that equivalent value in the divider equation.

Req = (R₁ RL) / (R₁ + RL)
Vₒ = Vᵢ × (Req) / (Req + R₂)

This is important because a connected load lowers the effective output-side resistance, which usually lowers the actual output voltage compared to the ideal no-load value.

Common Checks

  • If R1 and R2 are equal, the output is 50% of the input.
  • If R1 is much larger than R2, the output approaches the input voltage.
  • If R1 is much smaller than R2, the output becomes a small fraction of the input.
  • As R2 approaches zero, the output approaches the input. The widget requires finite positive resistor values and does not model a zero-resistance connection.

If Your Output Is Measured Across R2 Instead

Some circuit diagrams define the output across the other resistor. If that matches your setup, use the alternate divider form below or swap the resistor labels before using the calculator.

Vₒ = Vᵢ × (R₂) / (R₁ + R₂)

Common Applications

  • Reducing a higher source voltage to a lower reference voltage
  • Biasing transistor and amplifier inputs
  • Scaling signals for analog-to-digital converters
  • Creating sensor reference levels and threshold voltages
  • Building simple adjustable voltage networks with resistor changes