How to Calculate Voltage Dividers
Learn how to design a resistive voltage divider using the voltage divider formula. Covers output voltage calculation, loading effects, and practical design guidelines.
What a Voltage Divider Does
A voltage divider is a simple circuit consisting of two resistors in series that produces an output voltage (Vout) that is a fraction of the input voltage (Vin). It is one of the most fundamental building blocks in electronics, used for biasing transistors, scaling sensor outputs for ADC inputs, creating reference voltages, and level-shifting signals. The output is taken from the junction between the two resistors, and the ratio of the two resistances determines what fraction of Vin appears at Vout.
The Voltage Divider Formula
The output voltage of an unloaded voltage divider is: Vout = Vin × R2 / (R1 + R2), where R1 is the top resistor (between Vin and Vout) and R2 is the bottom resistor (between Vout and ground). To step 12 V down to 5 V: 5/12 = R2/(R1 + R2), so R2/(R1 + R2) = 0.4167. Choosing R2 = 10 kΩ gives R1 + R2 = 10,000/0.4167 = 24 kΩ, so R1 = 14 kΩ. Use 15 kΩ (standard value), giving Vout = 12 × 10/(15 + 10) = 4.8 V.
Solving for Resistor Values
To design a divider for a target Vout, choose a ratio k = Vout/Vin, then: R2 = k × R1 / (1 − k). You have freedom to choose R1, so pick a value that keeps the divider current (I = Vin/(R1+R2)) at a reasonable level — large enough to dominate load current, small enough to avoid wasting power. For a sensor biasing circuit, a total resistance of 10–100 kΩ is typical. For a high-precision reference, lower total resistance reduces the effect of leakage currents and noise.
The Loading Effect
When a load is connected to the Vout node, it forms a parallel combination with R2, changing the effective bottom resistance and pulling Vout down. The loaded output voltage is: Vout_loaded = Vin × (R2 ∥ Rload) / (R1 + R2 ∥ Rload). For the divider to behave close to ideal, the load resistance must be much greater than R2 — at least 10× greater is a common rule of thumb. If Rload = 10 × R2, the actual Vout drops by roughly 9% from the ideal value.
Designing for ADC Input Scaling
Microcontroller ADC inputs are typically rated for 0–3.3 V or 0–5 V, while sensors may output 0–10 V or 0–12 V. A voltage divider scales the sensor range down to the ADC range. For a 0–10 V sensor into a 0–3.3 V ADC: k = 3.3/10 = 0.33. Using R1 = 68 kΩ and R2 = 33 kΩ gives Vout = Vin × 33/(68+33) = Vin × 0.327, scaling 10 V to 3.27 V — close enough and within the ADC limit. The ADC input impedance (typically 1 MΩ or higher) keeps loading negligible.
Potentiometers as Adjustable Voltage Dividers
A potentiometer is a variable voltage divider with a sliding wiper contact. As the wiper moves, R1 and R2 change complementarily while R1 + R2 stays constant. The output voltage varies linearly (for linear taper) or logarithmically (for audio taper) with wiper position. Potentiometers are used as volume controls, position sensors, and manual tuning elements. When used as a voltage divider, connect all three terminals; using only two terminals makes it a variable resistor (rheostat).
Thevenin Equivalent of a Voltage Divider
Any voltage divider can be modeled as a Thevenin equivalent: a voltage source Vth in series with a resistance Rth. The Thevenin voltage is Vth = Vin × R2/(R1 + R2) (the open-circuit output voltage) and the Thevenin resistance is Rth = R1 ∥ R2 = (R1 × R2)/(R1 + R2). This model instantly shows how the divider will behave under any load: treat the load as connected to Vth through Rth and apply standard voltage divider analysis. Minimizing Rth (using lower resistor values) makes the divider stiffer and less affected by load variations.
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