Slant Height Calculator

What Is a Slant Height Calculator?

Slant height is the distance from the apex of a cone or pyramid down the sloped face to the edge of the base. The Slant Height Calculator works for right circular cones, regular square pyramids, truncated cones, and simple 2D slopes. It also reports surface area, volume, and slope angles where relevant.

How the Math Works

Each shape forms a right triangle, so the slant height is the hypotenuse of that triangle:

$$s = \sqrt{r^{2} + h^{2}} \quad \text{(cone)}$$

$$s = \sqrt{h^{2} + \left(\frac{a}{2}\right)^{2}} \quad \text{(square pyramid)}$$

$$s = \sqrt{h^{2} + (r_{2} - r_{1})^{2}} \quad \text{(conical frustum)}$$

$$s = \sqrt{x^{2} + y^{2}} \quad \text{(2D incline)}$$

For the cone, r is the base radius and h is the vertical height. For the pyramid, a is the base side length. For the frustum, r1 and r2 are the top and bottom radii.

Worked Example

A cone has a base radius of 3 cm and a vertical height of 4 cm:

$$s = \sqrt{3^{2} + 4^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ cm}$$

The calculator also returns a lateral area of about 47.12 cm squared and a volume of about 37.70 cm cubed.

Related free tools

For full solids, see the Cone Calculator, the Pyramid Calculator, and the Conical Frustum Calculator.