# Surface Area to Volume Ratio Calculator

URL: https://speedycalculator.com/calculators/math/surface-area-volume-ratio/
Last updated: 2026-10-30

> The surface area to volume ratio calculator finds the surface area, volume and SA:V ratio of a cube, box, sphere, cylinder, cone, hemisphere, capsule or square pyramid.

## Inputs

- Shape
- Side a (cm, m, mm, in, ft, yd, km, mi)
- Side b (cm, m, mm, in, ft, yd, km, mi)
- Radius r (cm, m, mm, in, ft, yd, km, mi)
- Height h (cm, m, mm, in, ft, yd, km, mi)

## Results

- Surface area
- Volume
- Surface area to volume ratio

## Formula

```
SA:V = surface area ÷ volume  (sphere 3/r, cube 6/a)
```

## Explanation

The surface-to-volume ratio explains why cells are small, why elephants have big ears, why crushed ice cools drinks faster and why nanoparticles are so reactive. As objects grow, volume outpaces surface.

### How to use the Surface Area to Volume Ratio Calculator

- **Shape**
- **Side a**
- **Side b**
- **Radius r**
- **Height h**

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

### How it works

Choose the shape and dimensions. The ratio has units of inverse length, so its value depends on the length unit.

### Inputs explained

FieldWhat to enterShapeChoose one: Cube, Rectangular box, Sphere, Cylinder …Side aUnits: cm, m, mm, in, ft, yd …Side bUnits: cm, m, mm, in, ft, yd …Radius rUnits: cm, m, mm, in, ft, yd …Height hUnits: cm, m, mm, in, ft, yd …

### Example values

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

Side a (cm)Surface area to volume ratio (cm⁻¹)233241.551.26180.75

## Worked example

Inputs — Shape: Cube; Side a: 4 cm.

Results — Surface area = 96 cm²; Volume = 64 cm³; **Surface area to volume ratio = 1.5 cm⁻¹**.

## Key terms

- **SA:V**: Surface area divided by volume.

## FAQ

**Why do cells stay small?**
A high SA:V lets nutrients and waste cross the membrane fast enough.

**Which shape has the lowest SA:V?**
A sphere, for a given volume.

**What units does the ratio have?**
Inverse length, e.g. cm⁻¹.

**How does SA:V change when I double the size?**
It halves.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Solid geometry](https://mathworld.wolfram.com/SolidGeometry.html)