How many litres does my bucket hold?

Measure the top and bottom diameters and the height, choose diameters and the unit, and the calculator gives the capacity in litres and US and UK gallons. It also lists how much is in the bucket at 25, 50, 75 and 90 percent of the height and tells you how deep to fill for a given volume.

Frustum Calculator

MiniWebtool’s Frustum Calculator finds volume, surface areas, and slant height for a truncated cone from its two radii and perpendicular height. A diagram and formula steps show how those measurements define the solid.

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Help me understand MiniWebtool's Frustum Calculator: https://miniwebtool.com/frustum-calculator/. What can I use it for, what inputs or settings do I need, and how do I use it and understand the output? Walk me through one simple example. Use this page as your source and answer in English.

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A frustum is a big cone minus the small cone cut off its top

Enter the bottom radius, top radius and height below to get the volume, slant height and surface areas, with the steps.

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About Frustum Calculator

The Frustum Calculator computes the volume, lateral surface area, total surface area, slant height, and centroid of a frustum (truncated cone). A frustum is formed when a cone is cut by a plane parallel to its base, producing a solid with two circular faces of different sizes. Enter the bottom radius (R), top radius (r), and height (h) to get instant results with step-by-step formulas and an interactive cross-section diagram.

At a Glance

Frustum Calculator finds the volume, lateral and total surface area, slant height and centroid of a frustum (truncated cone) from its two radii and height. Formula steps and a cross-section diagram are shown.

Frustum Calculator: features at a glance
Feature	What you get	Good for
Inputs	Enter the bottom and top measurements and the height. Measurements can be radii or diameters, and the height can be vertical or slant height.	Measuring a bucket or cup across its full width
Units	Choose none, mm, cm, m, inches or feet.	Matching the units of your measurements
Results	Returns volume V = pi h/3 (R^2 + Rr + r^2), lateral area, top and bottom base areas, total surface area and slant height.	Capacity and material estimates for tapered containers
Centroid	Gives the centroid height, measured from the larger base.	Balance and center-of-mass problems
Diagram overlays	An interactive cross-section can show dimensions, slant height, the full cone and the centroid.	Seeing how the frustum relates to the original cone
Quick examples	Buttons load a bucket, lampshade, cooling tower, cup or cone (r = 0). A top radius of 0 gives a cone, and equal radii give a cylinder.	Trying typical shapes before entering your own

Real-World Applications of Frustums

🪣

Buckets

Tapered shape for easy stacking

💡

Lampshades

Conical shade for directed light

🏗

Cooling Towers

Hyperboloid frustum shape

🥤

Cups & Glasses

Tapered for comfortable grip

🌺

Flower Pots

Wider base for stability

🎥

View Frustum

3D camera clipping volume

Key Formulas for a Frustum

For a frustum with bottom radius R, top radius r, and perpendicular height h:

Frustum Calculator: Key Formulas for a Frustum
Property	Formula	Description
Slant Height	\(l = \sqrt{h^2 + (R - r)^2}\)	Length along the lateral side
Volume	\(V = \frac{\pi h}{3}(R^2 + Rr + r^2)\)	Enclosed 3D space
Lateral Area	\(A_l = \pi(R + r) \times l\)	Curved side surface only
Top Base Area	\(A_{top} = \pi r^2\)	Smaller circular face
Bottom Base Area	\(A_{bot} = \pi R^2\)	Larger circular face
Total Surface Area	\(A_t = A_l + \pi R^2 + \pi r^2\)	All surfaces combined

Understanding Frustum Geometry

A frustum is created by slicing a right circular cone with a plane parallel to its base. The height h is the perpendicular distance between the two parallel circular faces. The slant height (l) is the distance along the lateral surface between the edges of the two bases — it is longer than h because it runs diagonally. When the top radius equals zero (r = 0), the frustum becomes a complete cone. When both radii are equal (R = r), the frustum becomes a cylinder.

How to Use the Frustum Calculator

Enter the bottom radius (R): Type the radius of the larger circular base, or click a quick example like Bucket, Lampshade, or Cup.
Enter the top radius (r): Type the radius of the smaller circular top. Set to 0 for a complete cone.
Enter the height (h): Type the perpendicular height of the frustum.
Click Calculate Frustum: Press the button to compute all properties instantly.
Review the results: See volume, surface areas, slant height, and centroid in the results cards. Toggle the diagram overlays to visualize dimensions, slant height, the original cone extension, and centroid location.

Frustum vs. Cone vs. Cylinder

A cone has one circular base and tapers to a point (apex). A cylinder has two equal circular bases connected by a straight lateral surface. A frustum sits between these two shapes: it has two unequal circular bases connected by a sloped surface. The frustum volume formula \(V = \frac{\pi h}{3}(R^2 + Rr + r^2)\) generalizes to the cone formula when r = 0 and to the cylinder formula when R = r.

Centroid of a Frustum

The centroid (center of mass for uniform density) of a frustum is located at height \(\bar{y} = \frac{h(R^2 + 2Rr + 3r^2)}{4(R^2 + Rr + r^2)}\) measured from the larger base. This is always closer to the larger base than to the smaller one, since more mass is concentrated near the wider end.

FAQ

What is a frustum?

A frustum is a portion of a solid, usually a cone, that lies between two parallel planes cutting it. When you slice the top off a cone with a plane parallel to the base, the remaining solid is called a frustum or truncated cone. It has two circular faces of different sizes connected by a sloped lateral surface.

How do you calculate the volume of a frustum?

The volume of a frustum is V = (π × h / 3)(R² + R × r + r²), where R is the bottom radius, r is the top radius, and h is the perpendicular height. This formula works for any frustum including the special cases where r = 0 (cone) or R = r (cylinder).

What is the lateral surface area of a frustum?

The lateral surface area of a frustum is A = π × (R + r) × l, where l is the slant height. The slant height is calculated as l = √(h² + (R − r)²). This gives the area of just the curved side surface, not including the top and bottom circular faces.

What is the difference between a frustum and a cone?

A cone tapers to a single point (apex), while a frustum is a cone with its top cut off by a plane parallel to the base, resulting in two circular faces of different sizes connected by a sloped lateral surface. A frustum with top radius r = 0 is a complete cone.

Where are frustums used in real life?

Frustums appear in many everyday objects: buckets, lampshades, drinking cups, flower pots, traffic cones, cooling towers, and architectural columns. In computer graphics, the view frustum defines the visible 3D space of a camera. In civil engineering, frustum shapes are used in foundation design and dam construction.

How much paint do I need for the curved side of a tapered planter?

Estimate the planter’s curved area with the lateral surface formula π(R + r)l, where R and r are the bottom and top radii and l is the slant height. For example, if the radii are 6 and 4 inches and the slant height is 10 inches, the curved area is about 314 square inches. Add the base areas only if you also plan to paint those circular faces.

Should I enter the diameter or radius of a bucket?

The calculator’s base measurements are radii, even though you may measure a bucket across its full width. Divide each measured diameter by 2 before entering it: a 12-inch bottom diameter means a 6-inch bottom radius. Use the bottom radius for the larger base and the top radius for the smaller base. Mixing diameter and radius can substantially change the calculated volume and surface areas.

What happens if a frustum’s top and bottom have the same radius?

If the top and bottom radii are equal, the shape is a cylinder. Its side is vertical, so the slant height equals the perpendicular height, and the lateral area becomes 2πRh. For example, a cylinder with radius 3 inches and height 8 inches has a lateral area of 48π, or about 150.8 square inches. The two circular ends are added separately for total surface area.

Reference this content, page, or tool as:

"Frustum Calculator" at https://MiniWebtool.com/frustum-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: 2026-04-02

Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs

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Gemini (copy & open)

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Help me understand MiniWebtool's Frustum Calculator: https://miniwebtool.com/frustum-calculator/. What can I use it for, what inputs or settings do I need, and how do I use it and understand the output? Walk me through one simple example. Use this page as your source and answer in English.

Frustum Calculator

About Frustum Calculator

At a Glance

Real-World Applications of Frustums

Key Formulas for a Frustum

Understanding Frustum Geometry

How to Use the Frustum Calculator

Frustum vs. Cone vs. Cylinder

Centroid of a Frustum

FAQ

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