Frustum Volume Calculator

On This Page

• How to use the Frustum Volume Calculator
• Conical frustum volume formula
• How to calculate volume of a frustum
• Frustum of a cone and special cases
• Pyramid, square, and rectangular frustums
• Worked examples
• Frustum volume units, liters, and gallons
• Frequently asked questions

How to Use the Frustum Volume Calculator

Use this frustum volume calculator for a tapered circular shape when you know the top radius, bottom radius, and vertical height. The page shows top area, bottom area, slant height, total surface area, liters, gallons, cubic feet, and steps.

Use it for tapered buckets, plant pots, lampshades, funnels, cone frustums, reducer fittings, and containers with two circular ends of different sizes.

Conical Frustum Volume Formula

The standard formula for calculating the volume of a conical frustum is:

• V = volume
• R = larger radius
• r = smaller radius
• h = vertical height between the two circular faces

The mixed term Rr is important. A frustum changes gradually from one radius to the other, so averaging two cylinders will not give the right formula.

How to Calculate Volume of a Frustum

To calculate frustum volume by hand, identify the two radii and the vertical height. Make sure all measurements use the same unit.

Step 1: Find Top and Bottom Radii

If the problem gives diameters, divide each diameter by 2. The formula works even if you call the larger radius top or bottom, but it is common to label the larger radius R.

Step 2: Square Each Radius

Calculate R² and r².

Step 3: Multiply the Radii Together

Calculate Rr. This term connects the larger and smaller circular faces.

Step 4: Add the Radius Terms

Add R² + Rr + r².

Step 5: Multiply by πh / 3

Multiply the sum by pi and height, then divide by 3. Write the answer in cubic units.

1. Find R, r, and h
2. Calculate R², Rr, and r²
3. Add the three terms
4. Multiply by πh / 3
5. Write the answer in cubic units

Frustum of a Cone and Special Cases

A conical frustum is also called a frustum of a cone or truncated cone. It is what remains when the top of a cone is cut off parallel to the base.

• If r = 0: the frustum becomes a cone.
• If R = r: the frustum becomes a cylinder.
• If the top and bottom are circles: use the conical frustum formula on this page.

Pyramid, Square, and Rectangular Frustums

A pyramid frustum volume calculator uses areas, not radii. This applies to frustums with square, rectangular, triangular, or polygonal parallel faces.

• A1 = area of one parallel face
• A2 = area of the other parallel face
• h = vertical height between the faces

For a square frustum, calculate each square area first. For a rectangular frustum, calculate the top rectangle area and bottom rectangle area first.

Worked Frustum Volume Examples

Tapered shapes should not be treated like plain cylinders. Check whether the shape is circular or pyramid-based before choosing a formula.

Example 1: Conical Frustum Plant Pot

Problem: A plant pot is shaped like a frustum of a cone. The top radius is 9 cm, the bottom radius is 5 cm, and the inside height is 14 cm. Estimate the internal volume.

1. R = 9 cm, r = 5 cm, h = 14 cm
2. R² = 81, Rr = 45, r² = 25
3. Sum = 81 + 45 + 25 = 151
4. V = π × 14 × 151 ÷ 3
5. V ≈ 2,213.98 cm³

Answer: The plant pot volume is about 2,214 cm³.

Example 2: Frustum of a Cone From a Cut Cone

Problem: A cone is cut parallel to its base, leaving a frustum with bottom radius 12 cm, top radius 4 cm, and height 18 cm. Find the volume.

1. R² = 12² = 144
2. Rr = 12 × 4 = 48
3. r² = 4² = 16
4. V = π × 18 × (144 + 48 + 16) ÷ 3
5. V ≈ 3,920.71 cm³

Answer: The cone frustum volume is about 3,920.7 cm³.

Example 3: Diameter Given Instead of Radius

Problem: A tapered container has top diameter 20 inches, bottom diameter 12 inches, and vertical height 15 inches. Find the volume.

1. Top radius = 20 ÷ 2 = 10 in
2. Bottom radius = 12 ÷ 2 = 6 in
3. R² + Rr + r² = 10² + 10 × 6 + 6² = 196
4. V = π × 15 × 196 ÷ 3
5. V ≈ 3,078.76 in³

Answer: The frustum volume is about 3,078.8 cubic inches.

Example 4: Square Pyramid Frustum

Problem: A square frustum has bottom side 10 cm, top side 6 cm, and vertical height 8 cm. Find the volume.

1. Bottom area A1 = 10² = 100 cm²
2. Top area A2 = 6² = 36 cm²
3. √(A1A2) = √(100 × 36) = 60
4. V = 8(100 + 36 + 60) ÷ 3
5. V = 522.67 cm³

Answer: The square frustum volume is about 522.7 cm³.

Example 5: Frustum Capacity in Liters

Problem: A conical frustum tank has bottom radius 0.8 m, top radius 0.5 m, and height 1.2 m. Estimate its capacity in liters.

1. R² + Rr + r² = 0.8² + 0.8 × 0.5 + 0.5² = 1.29
2. Volume = π × 1.2 × 1.29 ÷ 3
3. Volume ≈ 1.621 m³
4. Liters = 1.621 × 1,000 = 1,621 L

Answer: The frustum tank holds about 1,621 liters.

Frustum Volume Units, Liters, and Gallons

Frustum volume is written in cubic units. If the dimensions are in centimeters, the result is cm³. If the dimensions are in meters, the result is m³.

Frustum Volume Mistakes to Avoid

• Using diameter as radius: Divide diameter by 2 before calculating.
• Using slant height: Volume uses vertical height, not slant height.
• Averaging radii: The formula needs R², Rr, and r².
• Using the circular formula for a pyramid frustum: Square and rectangular frustums use the area-based formula.

Frequently Asked Questions

How do you calculate volume of a frustum?

For a conical frustum, use V = (πh / 3)(R² + Rr + r²). For a pyramid frustum, use V = h(A1 + A2 + √(A1A2)) / 3.

What is a conical frustum volume calculator?

It is a calculator for a cone with the top cut off. It uses top radius, bottom radius, and vertical height.

Is a frustum cone the same as a truncated cone?

Yes. A frustum of a cone is often called a truncated cone.

How do you calculate volume of a pyramid frustum?

Find the areas of the two parallel faces, then use V = h(A1 + A2 + √(A1A2)) / 3.

Can top radius and bottom radius be switched?

Yes. The formula works either way because it uses R², Rr, and r².