Introduction
Volume is the amount of space inside a 3D shape. Whether you need to find how much water fits in a tank, how much concrete fills a mold, or how much air is inside a ball, knowing the volume gives you the answer. Each shape has its own formula. A sphere uses V = (4/3)πr³, a cube uses V = a³, and a cylinder uses V = πr²h. Remembering every formula and doing the math by hand takes time and leaves room for mistakes.
This volume calculator finds the volume from the measurements you enter. It covers 12 common shapes: sphere, cone, cube, cuboid, cylinder, capsule, spherical cap, conical frustum, ellipsoid, square pyramid, tube, and general pyramid. Just pick a shape, type in your measurements, and choose your units. The tool gives you the volume in cubic meters right away, then converts it into cubic centimeters, liters, gallons, cubic feet, and more. You can switch between radius and diameter, mix different units across inputs, and compare all your results side by side on a bar chart. Hit "Calculate All" to update every shape at once, or let the calculator update live as you type.
How to Use Our Volume Calculator
Enter the measurements for any 3D shape below, and the calculator will give you the volume in cubic meters along with conversions to other units. You can calculate volume for all 12 shapes at once.
Sphere: Enter the radius or diameter of the sphere. Use the toggle to switch between radius and diameter input. Pick your unit of measurement from the dropdown.
Cone: Enter the radius (or diameter) of the base and the height of the cone. Toggle between radius and diameter as needed, and choose your preferred unit for each value.
Cube: Enter the side length of the cube. Since all sides of a cube are equal, only one measurement is needed. Select your unit from the dropdown.
Cuboid (Rectangular Prism): Enter the length, width, and height of the box shape. Each dimension can use a different unit if needed.
Cylinder: Enter the radius (or diameter) of the circular base and the height of the cylinder. Use the toggle to switch between radius and diameter.
Capsule: Enter the radius (or diameter) and the height of the cylindrical middle section only. The two rounded half-sphere ends are calculated automatically from the radius.
Spherical Cap: Enter any 2 of the 3 values: base radius (r), ball radius (R), or height (h). The calculator will figure out the missing third value and compute the volume for you.
Conical Frustum: Enter the top radius (r₁), bottom radius (r₂), and the height. You can toggle between radius and diameter input for both the top and bottom circles.
Ellipsoid: Enter the three semi-axis lengths: A, B, and C. These are the distances from the center to the surface along each of the three directions.
Square Pyramid: Enter the base edge length (one side of the square base) and the height from the base to the tip of the pyramid.
Tube (Hollow Cylinder): Enter the outer diameter, inner diameter, and the length of the tube. The inner diameter must be smaller than the outer diameter. The result shows the volume of the material only, not the hollow space inside.
Pyramid (General): Enter the base area in square units and the height. This works for any pyramid shape (triangular, pentagonal, or irregular) as long as you know the area of the base.
What Is Volume?
Volume is the amount of three-dimensional space that an object takes up. Think of it as how much water you would need to completely fill a shape. Volume is measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or liters (L). It is one of the most important measurements in math, science, and everyday life.
How Volume Is Calculated
Every 3D shape has its own formula for finding volume. These formulas use measurements like radius, height, length, and width. Here are the shapes covered by this calculator and how their volumes work:
- Sphere: A perfectly round ball. Its volume is V = (4/3)πr³, where r is the radius. The radius is the distance from the center to the edge.
- Cone: A shape with a circular base that narrows to a point. Its volume is V = (1/3)πr²h. A cone holds exactly one-third the volume of a cylinder with the same base and height.
- Cube: A box where all sides are equal. Its volume is simply V = a³, where a is the side length.
- Cuboid (Rectangular Prism): A box shape with different length, width, and height. Its volume is V = l × w × h.
- Cylinder: A shape like a can or pipe. Its volume is V = πr²h. You find the area of the circular base and multiply it by the height.
- Capsule: A cylinder with half-sphere caps on each end. Its volume combines a cylinder and a full sphere: V = πr²h + (4/3)πr³.
- Spherical Cap: A dome-shaped slice cut from a sphere. You only need two of the three values (base radius, ball radius, or height) to find its volume.
- Conical Frustum: A cone with the top cut off. Its formula is V = (πh/3)(r₁² + r₂² + r₁r₂), using both the top and bottom radii.
- Ellipsoid: A stretched or squished sphere, like an egg. Its volume is V = (4/3)πabc, where a, b, and c are the three semi-axes.
- Square Pyramid: A pyramid with a square base. Its volume is V = (1/3)a²h.
- Tube (Hollow Cylinder): A pipe shape with empty space inside. The volume of material equals the outer cylinder minus the inner cylinder.
- General Pyramid: Any pyramid shape where you already know the base area. Its volume is V = (1/3) × Base Area × h.
Why Volume Matters
Knowing how to find volume is useful in many real situations. You need volume when filling a swimming pool, shipping a package, pouring concrete, measuring medicine doses, or figuring out how much soil fits in a garden bed. Engineers, builders, scientists, and cooks all use volume calculations regularly. Construction professionals often need to convert volumes into cubic yards for ordering materials like gravel, sand, or mulch.
Tips for Accurate Results
Always make sure your measurements use the same unit before calculating. For example, if your radius is in centimeters and your height is in meters, the answer will be wrong. This calculator handles unit conversion automatically, so you can enter each measurement in whatever unit is easiest for you. It will convert everything to meters behind the scenes and then show results in ten different volume units, including liters, gallons, cubic feet, and more.
Remember that the radius is half the diameter. If you only know the diameter of a circle, you can switch the input mode from "Radius" to "Diameter" and enter it directly without doing the division yourself.