# Voltage Divider Calculator

> Computes the output voltage of a two-resistor divider (Vout = Vin·R2/(R1+R2)), the current through the chain and the power in each resistor, or solves for R2 when a target output voltage is given.

- Calculator id: `voltage-divider` · Category: Engineering & Automotive (`engineering`) · Tool name: `calculate_voltage_divider`
- Canonical page: https://tttkmbb.com/engineering/voltage-divider · This document: https://tttkmbb.com/engineering/voltage-divider.md · JSON definition: https://tttkmbb.com/engineering/voltage-divider.json

## Purpose

Computes the output voltage of a two-resistor divider (Vout = Vin·R2/(R1+R2)), the current through the chain and the power in each resistor, or solves for R2 when a target output voltage is given.

**Use when:** You need the voltage at the junction of two series resistors, the R2 that produces a target voltage, or the power each resistor must handle.

**Do not use when:** The output is loaded by a low-impedance load (the load parallels R2 and lowers Vout), you need a regulated supply, or you are limiting LED current (use led-resistor).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `input_voltage_v` | number | V | required | Voltage Vin applied across R1 + R2. (> 0, max 100000) |
| `r1_ohm` | number | Ω | required | Resistor between Vin and the output node, in ohms (1 kΩ = 1000). (> 0) |
| `r2_ohm` | number | Ω | optional | Resistor between the output node and ground. Omit and give target_output_voltage_v to solve for it. (> 0) |
| `target_output_voltage_v` | number | V | optional | Desired Vout; must be below input_voltage_v. Give either this or r2_ohm. (> 0) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `solved_for` | string |  | output_voltage_v when R2 was given, r2_ohm when the target voltage was given. |
| `output_voltage_v` | number | V | Vout = Vin × R2 / (R1 + R2) with no load. |
| `r2_ohm` | number | Ω | Bottom resistor (computed as R1 × Vout / (Vin − Vout) when solving). |
| `division_ratio` | number |  | Vout / Vin = R2 / (R1 + R2). |
| `current_ma` | number | mA | I = Vin / (R1 + R2), the quiescent current drawn from the source. |
| `power_r1_w` | number | W | I² × R1. |
| `power_r2_w` | number | W | I² × R2. |
| `total_power_w` | number | W | Vin × I. |
| `output_impedance_ohm` | number | Ω | Thévenin source resistance seen by a load: R1 ∥ R2 = R1 × R2 / (R1 + R2). |

## Formula

`output_voltage_v = input_voltage_v × r2_ohm / (r1_ohm + r2_ohm); r2_ohm = r1_ohm × target_output_voltage_v / (input_voltage_v − target_output_voltage_v); current = input_voltage_v / (r1_ohm + r2_ohm); power = current² × R`

Unloaded divider. A load RL across R2 replaces R2 by R2 ∥ RL; keep the output impedance at least 10 × smaller than the load for less than 10 % error.

## Data Sources

- Wikipedia – Voltage divider — https://en.wikipedia.org/wiki/Voltage_divider (reference, retrieved 2026-09-24)
- HyperPhysics – Voltage divider — http://hyperphysics.phy-astr.gsu.edu/hbase/electric/voldiv.html (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/voltage-divider?input_voltage_v=…&r1_ohm=…`
- `POST https://tttkmbb.com/api/v1/calculate/voltage-divider` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/voltage-divider · OpenAPI operationId `calculate_voltage_divider` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "voltage-divider", "inputs": {…}}`

## Example

- 12 V, R1 = 10 kΩ, R2 = 4.7 kΩ: inputs `{"input_voltage_v":12,"r1_ohm":10000,"r2_ohm":4700}` → `{"solved_for":"output_voltage_v","output_voltage_v":3.8367,"division_ratio":0.319728,"current_ma":0.8163,"power_r1_w":0.006664,"power_r2_w":0.003132,"total_power_w":0.009796,"output_impedance_ohm":3197.28}`
- 9 V to 5 V with R1 = 1 kΩ: inputs `{"input_voltage_v":9,"r1_ohm":1000,"target_output_voltage_v":5}` → `{"solved_for":"r2_ohm","r2_ohm":1250,"output_voltage_v":5,"current_ma":4,"power_r1_w":0.016,"power_r2_w":0.02}`

```
GET https://tttkmbb.com/api/v1/calculate/voltage-divider?input_voltage_v=12&r1_ohm=10000&r2_ohm=4700
```

## Limitations

The output is loaded by a low-impedance load (the load parallels R2 and lowers Vout), you need a regulated supply, or you are limiting LED current (use led-resistor). Unloaded divider. A load RL across R2 replaces R2 by R2 ∥ RL; keep the output impedance at least 10 × smaller than the load for less than 10 % error. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why does the voltage drop when I connect a load?**

The load is in parallel with R2, lowering the effective bottom resistance. Use resistors small enough that the output impedance is far below the load resistance, or add a buffer.

**Can I use a divider to power a circuit?**

Only for microamp loads or reference voltages; it wastes power continuously and the voltage sags with load. Use a regulator for supplies.

## Related

- [Ohm's Law Calculator](https://tttkmbb.com/physics/ohms-law.md) — Voltage, current and resistance for one resistor.
- [Resistors in Series and Parallel Calculator](https://tttkmbb.com/physics/resistors-series-parallel.md) — Equivalent resistance of the load in parallel with R2.
- [LED Resistor Calculator](https://tttkmbb.com/engineering/led-resistor.md) — Series resistor for an LED instead of a divider.