Voltage Divider Calculator
Answer
VOUT = VIN × R2 / (R1 + R2) when the tap is unloaded. The same current I = VIN / (R1 + R2) flows through both resistors. A load from the tap to ground sits in parallel with R2 and lowers VOUT. Size the divider current at least ten times the load current if you want the unloaded formula to stay honest.
Calculator
How it works
R1 and R2 share one current. The voltage at the tap is the drop across R2. Write VIN = I(R1 + R2) and VOUT = I·R2, cancel I, and you have the unloaded formula.
When a load hangs from the tap to ground it shares current with R2. Replace R2 with the parallel combination and reuse the same formula. The calculator reports both voltages so you can see how far the tap moved.
The current through R1 is always VIN / (R1 + R2′). Use it to size resistor power and to judge whether the divider is stiff enough for the load you actually have.
Parameters used on this page
| Parameter | Value | Source |
|---|---|---|
| Unloaded tap voltage | VOUT = VIN × R2 / (R1 + R2) | Ohm's law; Kirchhoff's current law at the tap |
| Divider current | I = VIN / (R1 + R2) | Ohm's law |
| Loaded tap | R2′ = R2 ∥ RLoad, then VOUT = VIN × R2′ / (R1 + R2′) | Parallel resistors, then the same divider formula |
| Power in each resistor | P = I²R for the resistor that carries I | Joule's law |
| Loading rule of thumb | Divider current ≥ 10 × load current | Common analogue-design practice so the tap stays close to the unloaded value |
| Preferred resistor values | IEC 60063 E12 / E24 / E96 decades | IEC 60063 |
Worked example
A 12 V rail, R1 = 10 kΩ (upper) and R2 = 10 kΩ (lower). Unloaded VOUT = 12 × 10k / 20k = 6.00 V. The divider current is 0.60 mA. Each resistor dissipates 3.6 mW. Hang a 10 kΩ load on the tap and R2′ becomes 5 kΩ, so VOUT falls to 4.00 V — the divider is only as stiff as its current.
Pitfalls
- Treating the unloaded formula as gospel when the next stage draws current. A microcontroller ADC pin is light; a 1 kΩ load is not.
- Using a divider as a power supply. It has no regulation. As the load changes, the tap moves.
- Ignoring resistor power on a high-voltage rail. At 24 V and 1 kΩ + 1 kΩ the pair dissipates 288 mW.
- Picking megaohm resistors to 'save current' and then wondering why the tap is noisy or slow.
FAQ
What is the voltage divider formula?
VOUT = VIN × R2 / (R1 + R2) for an unloaded tap, with R1 from the source to the tap and R2 from the tap to ground.
Which resistor is R1 and which is R2?
On this page R1 is the upper resistor (source to tap) and R2 is the lower resistor (tap to ground). Some texts swap the names; the algebra is the same if you keep the picture straight.
How do I choose R1 and R2 for 3.3 V from 5 V?
The ratio R2 / (R1 + R2) must be 3.3 / 5 = 0.66. One E24 pair is R1 = 5.1 kΩ and R2 = 10 kΩ (3.31 V unloaded). Then check that the divider current is large compared with whatever you hang on the tap.
Why did my measured voltage not match the formula?
The usual causes are a load on the tap, resistor tolerance, or a meter whose own resistance sits in parallel with R2.
Related
Sources
- Ohm's law and the definition of a series circuit.
- IEC 60063, Preferred number series for resistors and capacitors.