Math · Geometry
Frustum volume calculator.
Volume and surface area of a truncated cone or a square pyramid with the top cut off.
Inputs
Frustum
Enter your values.
How do you find the volume of a frustum?
A frustum is what is left of a cone or pyramid when the top is sliced off parallel to the base. For a cone frustum with bottom radius R, top radius r and height h, the volume is V = πh(R² + Rr + r²) / 3, the slant height is √((R − r)² + h²), and the lateral surface is π(R + r) × slant. Add the two circular faces for the total surface area. For any pyramid frustum, V = h(A₁ + A₂ + √(A₁A₂)) / 3 where A₁ and A₂ are the areas of the two parallel faces. Common uses are buckets, lampshades, flower pots, hoppers and concrete forms.
Worked example. A cone frustum with R = 4, r = 3 and h = 5 has a volume of 193.7315, a slant height of 5.099, a lateral area of 112.1333 and a total surface area of 190.6731. A square pyramid frustum with sides 6 and 4 and height 3 has a volume of 76.
Frequently asked questions
What is the formula for the volume of a frustum?
For a cone frustum, V = πh(R² + Rr + r²)/3. For a pyramid frustum, V = h(A₁ + A₂ + √(A₁A₂))/3 using the two face areas.
What is the difference between height and slant height?
Height is the perpendicular distance between the two faces. Slant height runs along the sloping side. For R = 4, r = 3, h = 5 the slant height is 5.099.
How do I find the volume of a bucket or planter?
Treat it as a cone frustum: measure the top and bottom inside radii (half the diameters) and the inside height, then read the volume. The units are the length unit cubed; for litres use centimetres and divide by 1,000.
Does the order of top and bottom matter?
Not for volume or surface area, since the formula is symmetric. Swap them and the answers do not change.
Sources
Checked
Cone frustum volume, slant height and lateral area are from the Conical Frustum page; the pyramid frustum volume formula is from the Pyramidal Frustum page. Total surface area adds the two face areas to the cited lateral area. The square pyramid lateral area is derived here as four trapezoids with face slant height sqrt(h^2 + ((a-b)/2)^2), not quoted from the page. Runs entirely in your browser. Nothing you type is sent or stored.
Scope
Results are exact mathematics rounded for display, so they are only as good as the measurements you enter. Any length unit works as long as every value uses the same one; areas come out in that unit squared and volumes in that unit cubed. For homework, DIY layout and estimating, not a substitute for a surveyor, engineer or your teacher's required method.