Truncated Cone Volume Calculator - Frustum Volume, Slant Height, and Area

A truncated cone volume calculator turns the larger base radius R, the smaller top radius r, and the perpendicular height h of a right circular frustum into its enclosed volume in real time.

• • Buckets and planters: Designers of tapered buckets, flower pots, and planters read off the fill volume in liters and US gallons.
• • Funnels and machine parts: Engineers sizing industrial funnels, hoppers, and tapered machine parts get the exact interior capacity.
• • Cooking and recipe scaling: Bakers scaling a bûche or a tiered mousse mold convert the top and bottom diameters into batter volume.
• • Geometry homework and exams: Students working through integration problems get an exact answer with side-by-side unit readouts.

A truncated cone (also called a frustum) is the slice of a cone that remains after the tip is cut off by a plane parallel to the base. Three numbers describe it: the larger radius R at the bottom, the smaller radius r at the top, and the perpendicular height h between the two circular faces.

Because the volume scales with the sum of the squares of the two radii and their product, even a small error in r shows up as a noticeable error in the result.

A truncated cone is just a full cone with its tip cut off, so it helps to keep the Cone Volume Calculator nearby for the r = 0 limit and for sanity checks.

The calculator applies the right circular frustum volume formula V = (πh/3)(R² + Rr + r²), derives slant height s = √((R − r)² + h²), and reports the lateral and total surface area so you can sanity-check the result.

• Larger base radius R: Radius of the larger circular base of the frustum.
• Smaller top radius r: Radius of the smaller circular top. Set to 0 to compute a full cone of base R and height h.
• Height h: Perpendicular distance between the two parallel circular bases of the frustum.
• Volume unit: Capacity unit used for the primary volume readout. The internal calculation always runs in cubic centimeters, and the chosen unit is applied at the end with an exact factor.

The formula is obtained by integrating the area of the circular cross-section as it changes linearly from radius R at the bottom to radius r at the top. The cross-sectional area at height y is π·[R + (r − R)(y/h)]², and integrating that from 0 to h gives (πh/3)(R² + Rr + r²).

The slant height s is the diagonal length along the slanted side, and the lateral surface area is π·(R + r)·s. Total surface area adds the two flat circular ends. According to Wolfram MathWorld, the volume of a right circular conical frustum is V = (πh/3)(R² + Rr + r²), and its slant height is s = √((R − r)² + h²), which is exactly the pair of relations this calculator uses.

According to Wolfram MathWorld, the volume of a right circular conical frustum is V = (πh/3)(R² + Rr + r²), and its slant height is s = √((R − r)² + h²).

When the two radii are equal the frustum becomes a cylinder, and the Cylinder Volume Calculator applies the simpler V = πR²h formula to the same shape.

These four ideas are enough to read every truncated cone volume formula you will meet in a textbook, a CAD package, or a slicer:

A useful intuition is to think of a truncated cone as a full cone with its tip sliced off. Set r = 0 to get the full cone V = (πh/3)·R²; set r = R to get a cylinder V = πR²h. The frustum formula returns both limits, which is why it is the most general version to memorize.

If you need to compare the frustum with a sphere, cone, or pyramid in the same design, the Volume Calculator gives you side-by-side volume calculations for any of those shapes.

Four short steps take you from three raw measurements to a complete frustum capacity readout:

1. 1 Measure the larger base radius R: Find the radius of the bigger of the two parallel circular faces. For a real object, divide the larger diameter by 2.
2. 2 Measure the smaller top radius r: Find the radius of the smaller parallel face. For a planter or funnel, divide the smaller opening diameter by 2.
3. 3 Enter the perpendicular height h: Measure straight up from the larger base to the smaller top, perpendicular to both faces.
4. 4 Pick a capacity unit: Choose cm³, m³, in³, ft³, L, or US gal from the dropdown. The other units stay visible for cross-checks.

For a tapered flower pot with R = 12 cm, r = 8 cm, and h = 18 cm, the calculator reports about 5,212 cm³ of soil volume (5.21 L, 1.38 US gal).

If you need the same number in a unit that is not on the dropdown, the Volume Converter extends the result to teaspoons, tablespoons, cups, quarts, and many more capacity units.

Why reach for an online truncated cone volume calculator instead of working the formula by hand each time?

• • Saves time on routine geometry: Replaces four to five manual steps with three input fields and a unit pick.
• • Capacity units side by side: Shows the same enclosed volume in cm³, L, and US gal at once, so the same number works for engineering specs, gardening, and fluid estimates.
• • Pairs volume with area and slant height: Reports the lateral and total surface area alongside the volume so you can size a mold, a liner, or a coating without leaving the page.
• • Covers full cones and cylinders: Setting r = 0 turns the frustum into a full cone, and setting r = R turns it into a cylinder.
• • Works in any length unit: Treats centimeters, meters, inches, and feet identically, so the same answer applies to metric drawings and imperial plans.

Type a new h, watch the volume update, switch the unit dropdown to US gal, and watch the readout change without leaving the page.

For a similar shape with flat trapezoid sides instead of a circular cross-section, the Trapezoidal Prism Volume Calculator applies the analogous cross-section-area-times-height idea to a prism.

The frustum volume formula looks short, but the four factors below decide whether the answer you compute matches the object in front of you:

• • The frustum volume formula assumes a right circular frustum with the two circular faces perfectly parallel. An oblique frustum cut at an angle or a shape with non-circular bases will not match the closed-form answer.
• • The volume returned is geometric. Real buckets, planters, and hoppers have wall thickness, taper imperfections, and interior fittings that change the true fill volume, so do not use the result to size a fluid tank without an extra safety margin.

Many product drawings list the diameter D = 2R and the diameter d = 2r, so you must divide each by 2 before entering the values. According to Wikipedia, the volume of a right circular frustum is V = (πh/3)(R² + Rr + r²), obtained by integrating the area of the circular cross-section that changes linearly from radius R to radius r over the height h.

According to Wikipedia, the volume of a right circular frustum is V = (πh/3)(R² + Rr + r²), obtained by integrating the area of the circular cross-section that changes linearly from radius R to radius r over the height h.

According to Encyclopaedia Britannica, a frustum is the portion of a cone or pyramid that lies between two parallel planes, and its volume is V = (h/3)(A₁ + A₂ + √(A₁·A₂)) for cross-sectional areas A₁ and A₂.

A pyramid is the polyhedral cousin of a cone, and the Triangular Pyramid Volume Calculator uses the same (1/3) · base area · height idea to size a triangular solid.