Voltage Divider Calculator
Design and analyze 2‑ and 3‑resistor voltage dividers, include load resistance, and solve backwards for resistor values from a target output voltage.
Voltage divider formula
A voltage divider is a pair (or chain) of resistors in series that scales an input voltage down to a lower output voltage. For the classic 2‑resistor divider with output taken across the bottom resistor R2:
Unloaded 2‑resistor divider
Input voltage: \( V_\text{in} \)
Resistors: R1 (top), R2 (bottom)
Output across R2:
\[ V_\text{out} = V_\text{in} \cdot \frac{R_2}{R_1 + R_2} \]
Divider current (no load):
\[ I_\text{div} = \frac{V_\text{in}}{R_1 + R_2} \]
With load resistance
Real dividers usually drive a load RL connected from Vout to ground. This load is in parallel with R2, reducing the effective resistance and pulling the output down.
Equivalent resistance of R2 in parallel with RL:
\[ R_\text{eq} = \left( \frac{1}{R_2} + \frac{1}{R_L} \right)^{-1} \]
Loaded output voltage:
\[ V_{\text{out, loaded}} = V_\text{in} \cdot \frac{R_\text{eq}}{R_1 + R_\text{eq}} \]
The calculator automatically switches to the loaded formula when you enter a finite RL.
Designing R1 and R2 for a target Vout
If you know Vin, desired Vout and a suitable total resistance \( R_\text{total} = R_1 + R_2 \), you can solve for R1 and R2:
From the divider equation:
\[ \frac{V_\text{out}}{V_\text{in}} = \frac{R_2}{R_1 + R_2} = \frac{R_2}{R_\text{total}} \]
So:
\[ R_2 = R_\text{total} \cdot \frac{V_\text{out}}{V_\text{in}}, \qquad R_1 = R_\text{total} - R_2 \]
The “Design for Target Vout” tab uses exactly this relationship.
3‑resistor voltage divider
A 3‑resistor chain gives you two different output voltages from the same Vin. With R1, R2, R3 in series from Vin to ground and no load:
Total resistance:
\[ R_\text{tot} = R_1 + R_2 + R_3 \]
Current (no load):
\[ I = \frac{V_\text{in}}{R_\text{tot}} \]
Voltages at the taps:
\[ V_{\text{out1}} = V_\text{in} \cdot \frac{R_2 + R_3}{R_\text{tot}}, \qquad V_{\text{out2}} = V_\text{in} \cdot \frac{R_3}{R_\text{tot}} \]
Practical design tips
- Keep divider current > load current. A common rule of thumb is to make the divider current 5–10× larger than the maximum load current so that loading only causes a small error.
- Check resistor power ratings. Power in each resistor is \( P = I^2 R \). Use at least a 2× safety margin over the calculated power.
- Watch input impedance of ADCs and op‑amps. High‑value dividers (hundreds of kΩ or more) may interact with input bias currents or sampling capacitors and distort the reading.
- Use lower values for noisy environments. Lower resistance values reduce susceptibility to noise pickup but increase power consumption.
Frequently asked questions
Can I use a voltage divider to power a device?
Only for very small, constant loads (e.g., reference pins). For powering logic or motors, use a proper regulator. A divider’s output voltage changes with load current and can become unstable or unsafe.
How small can the resistors be?
In principle you can use very small values, but the divider will draw a lot of current and waste power as heat. Check that the total current \( I = V_\text{in} / (R_1 + R_2) \) is acceptable for your supply and that each resistor’s power dissipation is below its rating.
How big can the resistors be?
Very large values reduce current and power, but make the output more sensitive to leakage currents, input bias currents, and noise. For microcontroller ADC inputs, dividers in the 10–100 kΩ range are common compromises.
Voltage Divider FAQ
What is a voltage divider?
A voltage divider is a simple resistor network that converts a higher DC voltage into a lower one using two or more resistors in series. The output is taken from a node between the resistors, giving a fixed fraction of the input voltage.
How do you calculate the output of a 2‑resistor voltage divider?
Use \( V_\text{out} = V_\text{in} \cdot \dfrac{R_2}{R_1 + R_2} \), where R1 is the resistor from Vin to Vout and R2 is from Vout to ground. This assumes the load on Vout is very large (negligible current).
How does load resistance affect a voltage divider?
A finite load RL in parallel with R2 lowers the effective resistance at the bottom of the divider, which reduces Vout. If RL is comparable to or smaller than R2, the output can drop significantly from the ideal value.
How do I choose resistor values for a voltage divider?
First determine the required ratio Vout/Vin. Then pick a convenient total resistance that gives a reasonable current (often 10–100 µA for low‑power references or 0.5–2 mA for ADC inputs). Compute R1 and R2 from the formulas, then round to the nearest standard E‑series resistor values and re‑check the resulting Vout.