Calculate Voltage Divider

Calculator and formula for calculating an unloaded voltage divider

Unloaded Voltage Divider

Input Options

For calculation, you need at least three known values:
• 2 voltage values + 1 resistance value
• 1 voltage value + 2 resistance values

Enter Voltages
Enter Resistances
Results
Voltages
Total voltage:
Voltage U₁:
Voltage U₂:
Resistances
Total resistance:
Resistance R₁:
Resistance R₂:

Voltage Divider Principle

Circuit diagram of an unloaded voltage divider with R1, R2 and the corresponding voltages

Circuit diagram: Unloaded voltage divider

Basic Principle

The voltage divider is a series circuit of two resistors:

  • Same current through both resistors
  • Voltage division proportional to the resistances
  • Utotal = U₁ + U₂
  • Rtotal = R₁ + R₂
Voltage Divider Formula
\[U_2 = U_{total} \cdot \frac{R_2}{R_1 + R_2}\]
Output voltage at the lower resistor
Typical Applications
  • Generate reference voltages
  • ADC voltage adaptation
  • Sensor interface circuits
  • Bias adjustment for amplifiers

Voltage Divider Formulas and Theory

1. Voltage divider formula

For the output voltage U₂:

\[U_2 = U_{total} \cdot \frac{R_2}{R_1 + R_2}\]

Proportional to resistance R₂

2. Calculation via current

Alternative calculation method:

\[I = \frac{U_{total}}{R_1 + R_2}\]
\[U_2 = R_2 \cdot I\]
3. Resistance calculation

From known voltages:

\[R_2 = \frac{U_2 \cdot R_1}{U_1}\]

When R₁ and voltages are known

Practical Calculation Examples

Example 1: Calculate voltage U₂

Given: Utotal = 12V, R₁ = 3kΩ, R₂ = 6kΩ

Find: Voltage U₂

\[U_2 = 12V \cdot \frac{6kΩ}{3kΩ + 6kΩ} = 12V \cdot \frac{6}{9} = 8V\]
Result: U₂ = 8V

✓ Check: U₁ = 4V, U₁ + U₂ = 12V ✓

Example 2: Calculate resistance R₂

Given: Utotal = 9V, U₂ = 3V, R₁ = 1kΩ

Find: Resistance R₂

U₁ = Utotal - U₂ = 9V - 3V = 6V
\[R_2 = \frac{U_2 \cdot R_1}{U_1} = \frac{3V \cdot 1kΩ}{6V} = 500Ω\]
Result: R₂ = 500Ω

✓ Ratio: 3V/6V = 500Ω/1000Ω = 1:2

Example 3: Generate reference voltage

Task: A reference voltage of 2V should be generated from 5V. R₁ = 1kΩ is given.

Find: Resistance R₂

From the voltage divider formula:
\[\frac{2V}{5V} = \frac{R_2}{1kΩ + R_2}\]
0.4 = R₂ / (1kΩ + R₂)
Solving: 0.4 × (1kΩ + R₂) = R₂
400Ω + 0.4 × R₂ = R₂
400Ω = 0.6 × R₂
R₂ = 667Ω (nearest standard value: 680Ω)

Check: With 680Ω: U₂ = 5V × (680Ω / 1680Ω) = 2.02V

Practical Applications and Design Guidelines

Common Applications

  • Reference voltages: Generation of stable reference voltages for analog circuits
  • ADC interfacing: Voltage adaptation for analog-to-digital converters
  • Sensor interfaces: Signal conditioning of sensor signals
  • Bias circuits: Operating point adjustment in amplifiers
  • Level converters: Adaptation between different logic levels
  • Measurement circuits: Voltage reduction for measuring instruments
Design Recommendations
  • Total resistance: 1kΩ - 100kΩ for typical applications
  • Load resistance: Should be at least 10x larger than R₂
  • Tolerances: Precision resistors (±1% or better) for accurate division
  • Temperature coefficient: Same TC values for both resistors
Comparison of Circuit Types
Circuit Type Characteristic Application
Unloaded voltage divider Constant division ratio Reference voltages, measurement circuits
Loaded voltage divider Division ratio changes with load Signal sources with variable load
Voltage regulator Constant output voltage Power supplies
Important Notes
  • Consider loading: Division ratio changes under load
  • Current consumption: Voltage dividers consume continuous current
  • Temperature drift: Resistance changes affect output voltage
  • Noise: Higher resistances generate more thermal noise
  • Frequency response: Parasitic capacitances can cause interference at high frequencies
Related Calculators

For applications with changing loads:

Loaded Voltage Divider
Practical Tips
  • Use metal film resistors for precision
  • Calculate power dissipation: P = U²/R
  • Buffer high-impedance outputs with operational amplifiers
  • Use bypass capacitors for RF applications


Circuits with resistors

Ohms Law  •  Total resistance of a resistor in parallel  •  Parallel- total resistance of 2 resistors  •  Series resistance for a voltmeter  •  Parallel resistance for an ampere meter  •  Voltage divider  •  Loaded voltage divider  •  Pi Attenuator  •  T Attenuator  •