Slant Height Calculator

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The slant height of a cone or pyramid is the distance measured along its slanted surface, from the apex down to the edge of the base — distinct from the vertical (true) height, which runs straight down through the shape's interior. It's the hypotenuse of a right triangle formed by the vertical height and either the base radius (for a cone) or half the base width (for a pyramid, measured to the midpoint of a base edge). This measurement is essential in construction and roofing (calculating the material needed for a conical or pyramidal roof surface, which is measured along the slant, not the vertical rise) and in manufacturing traffic cones, tents, and other conical or pyramidal objects.

How it works

Choose the shape, then enter the vertical height and the base measurement (radius for a cone, or half the base width for a pyramid). Because the vertical height, the horizontal base measurement, and the slant height form a right triangle — with the slant height as the hypotenuse — the Pythagorean theorem gives l = √(h² + b²).

Enter shape.
Enter height.
Enter radius (cone) or half-base-width (pyramid).
Click Calculate to see your results.

Examples

Cone: height = 4, radius = 3

l = √(4²+3²) = √(16+9) = √25 = 5 — a familiar 3-4-5 right triangle.

Square pyramid: height = 12, half base width = 5

l = √(12²+5²) = √(144+25) = √169 = 13.

Common mistakes to avoid

For a pyramid, using the full base width instead of half the base width.
Confusing slant height with vertical height and using the wrong one in a surface-area formula.
For a pyramid, confusing slant height (to an edge midpoint) with the lateral edge (to a corner) — they are different lengths.

Frequently asked questions

For a cone, yes — every point on the circular base is equidistant from the apex along the surface. For a pyramid, they're different: the slant height runs to the midpoint of a base edge, while the lateral edge runs all the way to a base corner, which is farther away — making the lateral edge longer than the slant height.

The right triangle used to find the slant height has its horizontal leg running from the pyramid's central axis to the midpoint of a base edge — which is half the base width away, not the full width.

A cone's lateral surface area is πrl (using slant height, not vertical height), and a pyramid's lateral faces are triangles whose area depends on the slant height as well — using the vertical height instead in these formulas would give an incorrect result.

No — since slant height is the hypotenuse of a right triangle that includes the vertical height as one leg, it must always be at least as long as the vertical height (and strictly longer whenever the base measurement is nonzero).

Free Slant Height Calculator