Voltage Divider Circuit
V_out = V_in × R₂/(R₁ + R₂). Two resistors in series divide voltage proportionally. Unloaded: exact; loaded: R_load affects output. Thevenin R_th = R₁∥R₂.
Did our AI summary help? Let us know.
Unloaded: V_out = V_in × R₂/(R₁ + R₂) Loaded: parallel combination R₂∥R_load reduces effective lower resistance R_th = R₁∥R₂; output impedance for load matching Power: P_R1 = V_R1²/R1; choose resistors for acceptable dissipation
Ready to run the numbers?
Why: Voltage dividers are ubiquitous: ADC references, sensor biasing, level shifting. Load resistance affects output; Thevenin equivalent simplifies analysis.
How: Enter R₁, R₂, V_in, and optional R_load. Calculator computes V_out, current, power dissipation, Thevenin equivalent, and load regulation.
Run the calculator when you are ready.
Enter Circuit Parameters
Basic Parameters
Load Parameters
Component Selection
Application
For educational and informational purposes only. Verify with a qualified professional.
🔬 Physics Facts
V_out/V_in = R₂/(R₁+R₂) when no load; ratio depends only on resistances.
— Ohm's law
Thevenin: V_th = V_out (open circuit), R_th = R₁∥R₂.
— Circuit theory
Load draws current; voltage drops. Use R_load >> R₂ for minimal effect.
— Loaded divider
Power in R₁ = V_R1²/R₁; total power = V_in²/(R₁+R₂) unloaded.
— Joule heating
What is a Voltage Divider?
A voltage divider is a fundamental passive circuit that produces an output voltage (Vout) that is a fraction of its input voltage (Vin). It consists of two resistors connected in series, with the output taken from the junction between them. Voltage dividers are one of the most commonly used circuits in electronics, found in applications ranging from sensor interfaces to ADC references.
Basic Operation
Two resistors in series divide the input voltage proportionally based on their resistance values.
Key Formula:
Vout = Vin × R2/(R1 + R2)
Load Effect
Connecting a load reduces output voltage due to parallel combination with R2, requiring careful design.
Design Rule:
RL should be >> R2 for minimal load effect
Thevenin Equivalent
Any voltage divider can be replaced by its Thevenin equivalent: a voltage source and series resistance.
Equivalent:
Vth = Vout, Rth = R1||R2
How Does a Voltage Divider Work?
A voltage divider works by applying Ohm's law and Kirchhoff's voltage law. When an input voltage is applied across two series resistors, the voltage drops proportionally across each resistor based on their resistance values. The output voltage is taken from the junction between the resistors, representing the voltage drop across the lower resistor (R2).
🔬 Circuit Analysis
Calculation Process
- 1Calculate total resistance: Rtotal = R1 + R2
- 2Calculate current: I = Vin / Rtotal
- 3Calculate output voltage: Vout = I × R2
- 4Simplify to: Vout = Vin × R2/(R1 + R2)
Key Principles
- Voltage divides proportionally to resistance
- Current is the same through both resistors
- Power dissipation must be considered
- Load resistance affects output voltage
When to Use Voltage Dividers
Voltage dividers are used in countless electronic applications. They're ideal when you need to reduce voltage levels, create reference voltages, interface different voltage levels, or provide bias voltages. However, they're not suitable for applications requiring high current or precise voltage regulation under varying loads.
ADC References
Converting higher voltage signals to ADC input range (e.g., 5V to 3.3V for microcontroller ADCs).
Key Consideration:
High input impedance ADC minimizes load effect
Sensor Interfaces
Scaling industrial sensor outputs (0-10V) to microcontroller input range (0-5V or 0-3.3V).
Key Consideration:
Maintain linearity and accuracy
Bias Voltages
Creating bias voltages for transistor biasing circuits and operational amplifier circuits.
Key Consideration:
Stable reference with minimal current draw
Level Shifting
Interfacing between different logic families (e.g., 3.3V to 1.8V, 5V to 3.3V).
Key Consideration:
Fast switching requires low output impedance
Audio Attenuators
Volume control and signal attenuation in audio circuits, providing precise level control.
Key Consideration:
Match impedance for audio applications
Voltage Divider Formulas
Understanding these formulas is essential for designing effective voltage divider circuits. Each formula addresses different aspects of circuit behavior, from basic voltage division to load effects and equivalent circuits.
📊 Core Formulas
Output Voltage (No Load)
Basic voltage divider formula for unloaded output
Current Through Circuit
Current is the same through both resistors in series
Output Voltage (With Load)
where R2 || RL = (R2 × RL)/(R2 + RL)
Accounts for load resistance parallel with R2
Thevenin Equivalent
Rth = (R1 × R2)/(R1 + R2)
Thevenin voltage and resistance for equivalent circuit
Power Dissipation
PR2 = I² × R2
PL = Vout²/RL (if load connected)
Power dissipation in each component
Frequently Asked Questions
What is a voltage divider and how does it work?
A voltage divider consists of two resistors in series. The output voltage is taken from the junction between them and equals Vout = Vin × R2/(R1 + R2). It works by dividing the input voltage proportionally based on the resistance values.
How does a load affect the output voltage?
Connecting a load resistance (RL) in parallel with R2 reduces the effective resistance, lowering the output voltage. The load effect is minimized when RL >> R2. For minimal load effect, use high-value resistors or buffer the output with an op-amp.
What is the Thevenin equivalent circuit?
The Thevenin equivalent replaces the voltage divider with a voltage source (Vth = Vout) and series resistance (Rth = R1||R2). This simplifies circuit analysis and represents the output impedance of the divider.
What resistor values should I use for a voltage divider?
Use resistor values that minimize power dissipation while maintaining acceptable load effect. Common values range from 1kΩ to 100kΩ. Higher values reduce power consumption but increase noise sensitivity. Lower values provide better load regulation but consume more power.
Can I use a voltage divider for power supply regulation?
Voltage dividers are not suitable for power supply regulation due to poor load regulation, high power dissipation, and lack of feedback. Use voltage regulators (linear or switching) for power supplies. Voltage dividers are best for signal level shifting and reference voltages.
How do I calculate power dissipation in resistors?
Power in each resistor is P = I² × R, where I = Vin/(R1 + R2). Total power is the sum of power in R1 and R2. Always select resistors with power ratings at least 2× the calculated power for safety margin.
What is the output impedance of a voltage divider?
The output impedance equals the Thevenin resistance: Rth = (R1 × R2)/(R1 + R2) = R1||R2. This represents the resistance seen looking back into the divider. Lower output impedance provides better load regulation but requires lower resistor values.
When should I use a voltage divider vs a voltage regulator?
Use voltage dividers for signal level shifting, ADC references, bias voltages, and low-current applications. Use voltage regulators for power supplies, high-current loads, and applications requiring stable voltage under varying loads. Regulators provide better regulation but are more complex.
📚 Official Data Sources
⚠️ Disclaimer
Circuit Design Disclaimer: This calculator provides estimates based on ideal circuit theory. Actual performance depends on component tolerances, temperature effects, parasitic capacitances, and real-world loading conditions. Always verify designs with circuit simulation and testing.
Component Selection: Resistor tolerances affect output voltage accuracy. Use precision resistors (0.1-1%) for critical applications. Power ratings must exceed calculated dissipation with adequate safety margin. Consider temperature coefficients for precision circuits.
Application Suitability: Voltage dividers are not suitable for power supply regulation or high-current applications. For such applications, use proper voltage regulators. This tool is for educational and preliminary design purposes. Professional engineering review is recommended for production designs.
Related Calculators
Parallel Resistor Calculator
Calculate equivalent parallel resistance, current division, power distribution, and thermal analysis for resistors connected in parallel. Supports up to 10...
PhysicsSeries Resistor Calculator
Calculate total series resistance, voltage division, power distribution, and thermal analysis for series resistor circuits. Supports up to 10 resistors with...
PhysicsVoltage Drop Calculator
Calculate voltage drop in electrical circuits with NEC compliance checking, wire gauge selection, power loss analysis, and comprehensive electrical...
PhysicsCapacitors in Series Calculator
Calculate equivalent capacitance, voltage division, charge distribution, and energy storage for capacitors connected in series. Includes AC analysis, safety...
PhysicsConductivity to Resistivity Calculator
Comprehensive calculator for converting between electrical conductivity and resistivity, calculating wire resistance, and analyzing temperature effects....
PhysicsHP to Amps Calculator
Convert horsepower to amperage for DC, single-phase AC, and three-phase AC motors. Includes wire sizing recommendations, voltage drop calculations, starting...
Physics