Pyramid Calculator
Calculate volume, slant height, lateral surface area, and total surface area of a pyramid with various base shapes.
Dimensions
Updates as you typeMode
What do you want to solve for? ?
Target volume ?
—
cm³
Display (units apply to every dimension)
Unit
Base
Base shape ?
Side length ?
—
cm
Length ?
—
cm
Width ?
—
cm
Base area ?
—
cm²
Base perimeter (optional) ?
—
cm
Height
Pyramid height ?
—
cm
Shape preview
square pyramidHow volume scales with height
Base fixed, height sweptHeight —
Volume —
Surface —
Volume
Surface area
Current height
Compare base shapes
Same side + height, different base| Base | Base area | Volume | Surface area | Volume relative |
|---|
Formula
V
=
1
3
×
A
×
h
SA
=
A
+
1
2
×
P
×
l
,
l
=
√
(
h²
+
a²
)
- V
- Volume of the pyramid
- SA
- Total surface area (base + lateral faces)
- A
- Area of the base polygon
- P
- Perimeter of the base
- h
- Perpendicular height from apex to base
- a
- Apothem — distance from base centre to an edge midpoint
- l
- Slant height along a face, from apex to base-edge midpoint
Worked example — your numbers
- Base area A = —
- Base perimeter P = —
- Apothem a = —
- Slant l = √(h² + a²) = —
- Lateral surface = ½ × P × l = —
- Volume V = ⅓ × A × h = —
- Surface SA = A + lateral = —
The apothem is only defined for regular polygons; for rectangles the formula uses min(length, width) / 2 as an approximation, and for fully custom bases you need to supply the perimeter explicitly for slant and lateral area to be computed.