Joule's Law | Engineering Calculator API

Joule's Law (Heating) API

Solve heat dissipated, current, resistance, voltage, power, or time using Joule's Law of Heating. This endpoint is designed for physics, electrical engineering, and circuit analysis calculations.

Law

$Q = I^2 R t$

Equivalent supported forms:

$Q = \frac{V^2 t}{R}$

$Q = V I t$

$Q = P t$

Request Body Example

1{
2  "law": "joule",
3  "vars": {
4    "Q": null,
5    "I": null,
6    "R": null,
7    "t": null,
8    "t_i": null,
9    "t_f": null,
10    "V": null,
11    "P": null
12  }
13}

Variables

You may provide either t or both t_i and t_f. The API computes $\Delta t = t_f - t_i$.

What the API Solves

The API solves for exactly one unknown. It will automatically derive relationships between:

• $V = IR$

• $P = IV = I^2R = \frac{V^2}{R}$

This means you can supply any valid combination of voltage, current, resistance, or power.

Example Requests

Heat dissipated by a resistor

1{
2  "law": "joule",
3  "vars": {
4    "I": 2,
5    "R": 10,
6    "t": 60
7  }
8}

Solve for time given heat

1{
2  "law": "joule",
3  "vars": {
4    "Q": 5000,
5    "I": 3,
6    "R": 50
7  }
8}

Using voltage instead of current

1{
2  "law": "joule",
3  "vars": {
4    "V": 120,
5    "R": 60,
6    "t": 3600
7  }
8}

Using power directly

1{
2  "law": "joule",
3  "vars": {
4    "P": 100,
5    "t_i": 0,
6    "t_f": 30
7  }
8}

Example Response

1{
2  "solved": "Q",
3  "value": 1200,
4  "summary": "Q = I²·R·Δt = 1200 J",
5  "inputs": {
6    "Q": null,
7    "I": 2,
8    "R": 10,
9    "V": 20,
10    "P": null,
11    "delta_t": 60,
12    "t_i": null,
13    "t_f": null
14  },
15  "derived": {
16    "power": 40,
17    "power_str": "40 W"
18  }
19}

Behavior Notes

• If one variable is missing, the API solves for it.

• If all variables are provided, the API verifies consistency.

• Division by zero (e.g. $R=0$ or $P=0$ when solving for time) will raise an error.

• If insufficient data is provided, the API returns a validation error.

Use Cases

• Electrical heating calculations

• Resistor power dissipation

• Energy loss in circuits

• Power and time consumption analysis

• Physics homework and engineering design

This endpoint is a core tool for circuit analysis, electronics education, and engineering workflows.