# Latus Rectum Calculator

URL: https://speedycalculator.com/calculators/math/latus-rectum/
Last updated: 2026-10-30

> The latus rectum calculator finds the length of the latus rectum (the focal chord perpendicular to the axis) of a parabola, ellipse or hyperbola, together with the focus and the endpoints.

## Inputs

- Shape
- A
- B
- C
- Semi-major axis a
- Semi-minor axis b
- Centre h
- Centre k

## Results

- Latus rectum length
- Focus – x
- Focus – y
- Endpoint 1 – x
- Endpoint 1 – y
- Endpoint 2 – x
- Endpoint 2 – y

## Formula

```
Parabola y = Ax² + Bx + C: length = 1/|A|
Ellipse / hyperbola: length = 2b²/a, foci at h ± c with c = √(a² ∓ b²)
```

## Explanation

The latus rectum is a chord through a focus, perpendicular to the main axis. Its length measures how "wide" a conic is at the focus and appears in orbital mechanics (the semi-latus rectum p sets the size of an orbit).

### How to use the Latus Rectum Calculator

- **Shape**
- **A**
- **B**
- **C**
- **Semi-major axis a**
- **Semi-minor axis b**
- **Centre h**
- **Centre k**

Results update as you type, and everything is calculated in your browser.

### How it works

For a parabola the focus lies 1/(4A) from the vertex and the latus rectum is 4 times that distance. For an ellipse or hyperbola with semi-axes a and b, the half-length b²/a is the semi-latus rectum.

### Inputs explained

FieldWhat to enterShapeChoose one: Parabola y = Ax² + Bx + C, Ellipse (horizontal), Hyperbola (horizontal)AA numberBA numberCA numberSemi-major axis aA numberSemi-minor axis bA numberCentre hA numberCentre kA number

### Example values

How the main result changes when **A** changes and everything else stays at the example values above:

ALatus rectum length0.12580.18755.33330.2540.31253.20.3752.66670.52

## Worked example

Inputs — Shape: Parabola y = Ax² + Bx + C; A: 0.25; B: -1; C: 3.

Results — **Latus rectum length = 4**; Focus – x = 2; Focus – y = 3; Endpoint 1 – x = 0; Endpoint 1 – y = 3; Endpoint 2 – x = 4; Endpoint 2 – y = 3.

## Key terms

- **Latus rectum**: The focal chord perpendicular to the axis of a conic.

## FAQ

**What is the latus rectum of y² = 4ax?**
4a.

**What is the semi-latus rectum?**
Half the latus rectum; for orbits it is p = b²/a.

**Does a circle have a latus rectum?**
Yes – it is the diameter (2r), since a = b = r.

**Why does the ellipse use a² − b² and the hyperbola a² + b²?**
Those give the focal distance c in each case.


## Sources

- [OpenStax – Precalculus 2e](https://openstax.org/details/books/precalculus-2e)
- [Wolfram MathWorld – Latus rectum](https://mathworld.wolfram.com/LatusRectum.html)