# Cone Calculator

URL: https://speedycalculator.com/calculators/math/cone/
Last updated: 2026-10-25

> The cone calculator finds the volume, slant height, lateral area and total surface area of a right circular cone from its base radius and height.

## Inputs

- Base radius (m, cm, mm, km, in, ft, yd, mi)
- Height (m, cm, mm, km, in, ft, yd, mi)

## Results

- Volume
- Slant height
- Lateral area
- Total surface area

## Formula

```
V = ⅓ π r² h
Slant height = √(r² + h²)
```

## Explanation

A cone holds exactly one third of the volume of a cylinder with the same base and height.

### How to use the Cone Calculator

- **Base radius**
- **Height**
- Want to work backwards? Type a value into **Volume** and **Height** is calculated for you.

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Multiply the base area by the height and divide by three. Pythagoras gives the slant height.

### Inputs explained

FieldWhat to enterBase radiusUnits: m, cm, mm, km, in, ft …HeightUnits: m, cm, mm, km, in, ft …

### What each result means

- **Volume** = pi×[Base radius]^2×[Height]÷3
- **Slant height** = sqrt([Base radius]^2 + [Height]^2)
- **Lateral area** = pi×[Base radius]×[Slant height]
- **Total surface area** = pi×[Base radius]×([Base radius] + [Slant height])

### Example values

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

Height (m)Volume (m³)218.85328.27437.7547.12656.55875.4

## Worked example

Inputs — Base radius: 3 m; Height: 4 m.

Results — **Volume = 37.7 m³**; Slant height = 5 m; Lateral area = 47.12 m²; Total surface area = 75.4 m².

## FAQ

**Is this for a party hat?**
The lateral area tells you how much paper you need.

**What about a truncated cone?**
Use the frustum formula: V = ⅓πh(R² + Rr + r²).

**What formula does the Cone Calculator use?**
V = ⅓ π r² h.

**Can I work backwards from the result?**
Yes. Type the result you want into Volume and the calculator finds the matching height.