PhysicsSolver360 logoPhysicsSolver360°
Powered by Solver360°

Voltage Divider Calculator

Find output voltage and current in a two-resistor voltage divider

Parameters

Vⓘ
Ωⓘ
Ωⓘ
Show Trail

Controls

xⓘ

Calculated Values

Output Voltage:
8.00;V8.00;V
Circuit Current:
0.00;A0.00;A
Power in R₁:
0.02;W0.02;W

Examples

12 V, 1 kΩ + 2 kΩ

Output across 2 kΩ.

  • Output Voltage: 8.008.00

5 V, equal 10 kΩ resistors

Half supply at midpoint.

  • Output Voltage: 2.502.50

Visualization

Voltage Divider — Potential Division in Series Resistors

A voltage divider (potential divider) is two or more resistors in series across a voltage source. The output voltage is taken across one resistor — typically R₂ between the junction and ground.

Because resistors are in series, the same current I = V_in/(R₁+R₂) flows through both. Ohm's law on R₂ gives V_out = I·R₂ = V_in·R₂/(R₁+R₂).

The fraction of input appearing at output is the voltage divider ratio: η = R₂/(R₁+R₂). For R₁ = R₂, V_out = V_in/2. For R₂ >> R₁, V_out → V_in; for R₂ << R₁, V_out → 0.

Loading effect: a real load R_L in parallel with R₂ reduces effective resistance R₂||R_L, lowering V_out. Design rule: R_L >> R₂ (often 10×–100×) for less than ~10% error.

Thevenin equivalent at output: V_th = V_out (open circuit) and R_th = R₁||R₂. Use this when analyzing loaded dividers or connecting to amplifier inputs.

Power: P₁ = I²R₁ and P₂ = I²R₂. Total P = V_in²/(R₁+R₂). Lower current (larger resistors) saves power but increases sensitivity to loading and noise.

Key Concepts

  • V_out = V_in × R₂/(R₁ + R₂)
  • I = V_in/(R₁ + R₂) — identical in both resistors
  • Divider ratio η = R₂/(R₁+R₂)
  • Loaded output: use R₂_eff = R₂∥R_L
  • Thevenin: V_th = V_out, R_th = R₁∥R₂
  • Never exceed V_in with passive resistors only

Real-World Applications

  • Microcontroller ADC reference scaling (0–3.3 V from 5 V)
  • Transistor base biasing networks
  • Potentiometer as adjustable divider
  • Sensor signal conditioning
  • Logic level translation between IC families

Explore Further

More electricity tools

  • Ohm's Law

    Calculate voltage, current, and resistance in electrical circuits.

  • Capacitance

    Analyze charge storage and electric fields in capacitors.

  • RC Circuits

    Calculate charging and discharging of capacitors in circuits.

  • Power Calculator

    Calculate electrical power, energy consumption, and efficiency.

  • Series Circuit

    Analyze series circuits with total resistance, current, and voltage drops.

  • Parallel Circuit

    Analyze parallel circuits with current division and total resistance.

Physics Equations

Output Voltage:
Vout=VinR2R1+R2V_{out} = V_{in} \frac{R_2}{R_1 + R_2}
Current:
I=VinR1+R2I = \frac{V_{in}}{R_1 + R_2}

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Recognize Circuit Topology

R₁ and R₂ are in series; V_out is taken across R₂.

Explanation:

Current has only one path: through R₁, then R₂. Output voltage is the potential drop across R₂.

2

Step 2: Total Series Resistance

Equation:

Rtotal=R1+R2R_{total} = R_1 + R_2

Calculation:

Rtotal=1000+2000=3000 ΩR_{total} = 1000 + 2000 = 3000 \text{ Ω}

Result:

Rtotal=3000ΩR_total = 3000 Ω

Explanation:

Series resistances add directly because the same current passes through each.

3

Step 3: Find Series Current (Ohm's Law)

Equation:

I=VinRtotalI = \frac{V_{in}}{R_{total}}

Calculation:

I=123000=0.004000 AI = \frac{12}{3000} = 0.004000 \text{ A}

Result:

I=0.004000AI = 0.004000 A

Explanation:

This current flows through both R₁ and R₂ (and would flow through any series elements).

4

Step 4: Voltage Across R₂

Equation:

Vout=I×R2V_{out} = I \times R_2

Calculation:

Vout=0.004000×2000=8.000000 VV_{out} = 0.004000 \times 2000 = 8.000000 \text{ V}

Result:

Vout=8.000000VV_out = 8.000000 V

Explanation:

Ohm's law on R₂ gives the output voltage directly from current and resistance.

5

Step 5: Verify with Divider Formula

Equation:

Vout=Vin×R2R1+R2V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2}

Calculation:

Vout=12×20003000=12×0.6667=8.000000 VV_{out} = 12 \times \frac{2000}{3000} = 12 \times 0.6667 = 8.000000 \text{ V}

Result:

Dividerratioη=66.67Divider ratio η = 66.67%

Explanation:

The fraction R₂/(R₁+R₂) is the voltage divider ratio — useful for design without finding current first.

6

Step 6: Power Dissipation (Optional Check)

Equation:

P=I2RP = I^2 R

Calculation:

P1=0.0160 W,P2=0.0320 W,Ptotal=0.0480 WP_1 = 0.0160 \text{ W}, \quad P_2 = 0.0320 \text{ W}, \quad P_{total} = 0.0480 \text{ W}

Explanation:

Total power from source equals V_in × I. Power splits between resistors proportionally to resistance.

Frequently Asked Questions (FAQ)

Can I get V_out > V_in?

Not with a passive two-resistor divider. Active circuits (op-amps) can boost voltage.

What resistor values should I choose?

Balance: lower R → more current and power; higher R → more loading sensitivity. Often 1 kΩ–100 kΩ for signals.

Why is my measured V_out lower than calculated?

Usually loading (meter or next stage draws current) or tolerance in R₁, R₂.

Three-resistor divider?

Chain dividers: treat each tap similarly; V at each node = V_in × (resistance below node)/(total R).

Does frequency matter?

At DC and low frequency, yes. At high frequency, parasitic capacitance can form another divider with R.

Practice MCQs

  1. With fixed R₁, increasing R₂ will:
  2. If R₁ = R₂ = 1 kΩ and V_in = 12 V, then V_out is:
  3. A heavy load (small R_L) in parallel with R₂ tends to:
  4. Current through R₁ and R₂ in an unloaded divider is:
  5. V_out can never be greater than V_in because:
  6. Thevenin resistance seen at V_out terminals is:

Related Calculators

These tools connect to the same physics concepts used in this calculator.

Coulomb's LawCalculate electrostatic force between point charges with animated field visualization.Wheatstone BridgeCheck bridge balance and calculate unknown resistance from ratio arms.ResistivityCalculate wire resistance from resistivity, length, and cross-sectional area.Capacitor EnergyFind stored charge and energy U = ½CV² with charging animation.Magnetic FieldCalculate magnetic field strength, magnetic force, and magnetic flux using Ampere's Law.Related Magnetism topic.Error PropagationCombine measurement uncertainties for sums, products, quotients, and powers in experimental formulas.Related Measurement & Uncertainty topic.Wave PropertiesCalculate wavelength, frequency, amplitude, and wave velocity.Related Waves topic.