# Ohm's Law Calculator

> Solves Ohm's law V = I·R for whichever of voltage, current or resistance is omitted and reports the electrical power dissipated (P = V·I).

- Calculator id: `ohms-law` · Category: Physics (`physics`) · Tool name: `solve_ohms_law`
- Canonical page: https://tttkmbb.com/physics/ohms-law · This document: https://tttkmbb.com/physics/ohms-law.md · JSON definition: https://tttkmbb.com/physics/ohms-law.json

## Purpose

Solves Ohm's law V = I·R for whichever of voltage, current or resistance is omitted and reports the electrical power dissipated (P = V·I).

**Use when:** You know two of voltage, current and resistance in a DC or purely resistive circuit and need the third and the power.

**Do not use when:** The load is reactive (inductors or capacitors require impedance, not resistance), you want energy cost over time (use electric-power), or you need the equivalent resistance of several resistors (use resistors-series-parallel).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `voltage_v` | number | V | optional | Potential difference across the component in volts. Omit to solve for it. (min 0) |
| `current_a` | number | A | optional | Current through the component in amperes (1 mA = 0.001 A). Omit to solve for it. (min 0) |
| `resistance_ohm` | number | Ω | optional | Resistance in ohms (1 kΩ = 1000 Ω). Omit to solve for it. (> 0) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `solved_for` | string |  | Which quantity was computed: voltage_v, current_a or resistance_ohm. |
| `voltage_v` | number | V | V = I × R. |
| `current_a` | number | A | I = V / R. |
| `current_ma` | number | mA | Current in milliamperes. |
| `resistance_ohm` | number | Ω | R = V / I. |
| `power_w` | number | W | Power dissipated P = V × I. |

## Formula

`V = I × R; I = V / R; R = V / I; P = V × I = I² × R = V² / R`

## Data Sources

- HyperPhysics – Ohm's law — http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmlaw.html (reference, retrieved 2026-09-23)
- Wikipedia – Ohm's law — https://en.wikipedia.org/wiki/Ohm%27s_law (reference, retrieved 2026-09-23)

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/ohms-law?`
- `POST https://tttkmbb.com/api/v1/calculate/ohms-law` 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/ohms-law · OpenAPI operationId `solve_ohms_law` 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: `solve_ohms_law` (dedicated) or `run_calculator` with `{"calculator_id": "ohms-law", "inputs": {…}}`

## Example

- 12 V across 220 Ω: inputs `{"voltage_v":12,"resistance_ohm":220}` → `{"solved_for":"current_a","current_a":0.054545,"current_ma":54.545,"power_w":0.6545}`
- 2 A through 50 Ω: inputs `{"current_a":2,"resistance_ohm":50}` → `{"solved_for":"voltage_v","voltage_v":100,"power_w":200}`

```
GET https://tttkmbb.com/api/v1/calculate/ohms-law?voltage_v=12&resistance_ohm=220
```

## Limitations

The load is reactive (inductors or capacitors require impedance, not resistance), you want energy cost over time (use electric-power), or you need the equivalent resistance of several resistors (use resistors-series-parallel). All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Does Ohm's law apply to AC circuits?**

Only for purely resistive loads. With inductance or capacitance the relation becomes V = I·Z with complex impedance Z, and the power depends on the phase angle.

**Why does the power matter?**

A resistor must be rated above the dissipated power (e.g. 0.65 W needs at least a 1 W resistor) or it overheats.

## Related

- [Electric Power Calculator](https://tttkmbb.com/physics/electric-power.md) — Power, energy and running cost of an appliance.
- [Resistors in Series and Parallel Calculator](https://tttkmbb.com/physics/resistors-series-parallel.md) — Equivalent resistance of several resistors.