Volume Calculator
MathCalculate the volume and surface area of cubes, spheres, cylinders, cones, and rectangular prisms. Enter dimensions and get precise 3D shape measurements.
Volume
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Surface Area
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What is a Volume?
A Volume Calculator works out the total space enclosed inside a 3D shape — cube, sphere, cylinder, cone, or rectangular prism — based on its dimensions, along with the shape's total outer surface area. Volume problems show up constantly in everyday and academic contexts: how much water a tank holds, how much concrete fills a cylindrical post, or how much a storage box can contain.
This calculator handles five of the most commonly needed 3D shapes in one tool, so you don't need to remember five separate formulas. It complements the Surface Area Calculator and the 2D-focused Area Calculator for a complete set of geometry tools.
How to use this Volume calculator
- Select the Shape you want to calculate — Cube, Sphere, Cylinder, Cone, or Rectangular Prism.
- Enter Dimension 1 — the side length for a cube, or the radius for a sphere, cylinder, or cone.
- For cylinders and cones, enter Dimension 2 as the height.
- For a rectangular prism, enter all three dimensions — length, width, and depth.
- Read the Volume result, the primary figure for most use cases.
- Check the Surface Area result if you also need to know the shape's outer covering area.
Formula & Methodology
Each shape uses its own standard geometry formula: - Cube: V = s³, Surface Area = 6s² - Sphere: V = (4/3)πr³, Surface Area = 4πr² - Cylinder: V = πr²h, Surface Area = 2πr² + 2πrh - Cone: V = (1/3)πr²h, Surface Area = πr² + πr × slant height (where slant height = √(r² + h²)) - Rectangular Prism: V = l × w × h, Surface Area = 2(lw + lh + wh) Worked example: for a cylinder with radius 5 and height 10: - Volume = π × 5² × 10 = π × 250 ≈ 785.4 cubic units - Surface Area = 2π × 5² + 2π × 5 × 10 = 157.1 + 314.2 ≈ 471.2 square units
Frequently Asked Questions
The volume of a cube is calculated as V = s³, where s is the length of one side. For example, a cube with a 4 cm side has a volume of 4³ = 64 cubic centimetres.
The volume of a sphere is calculated as V = (4/3)πr³, where r is the radius. This formula gives the total space enclosed by a perfectly round 3D shape, such as a ball.
A cylinder's volume is calculated as V = πr²h, where r is the radius of the circular base and h is the height. This is the same as finding the circular base's area and multiplying it by the height.
A cone's volume is exactly one-third of a cylinder with the same base radius and height: V = (1/3)πr²h. This is why a cone-shaped container holds noticeably less than a cylinder of the same width and height.
Volume measures the total space enclosed inside a 3D shape (in cubic units), while surface area measures the total area covering the outside of that shape (in square units). This calculator shows both together, since many real-world tasks need one or the other depending on whether you're filling a space or covering it.
A rectangular prism's (box's) volume is simply length × width × height. Select 'Rectangular Prism' and enter the three dimensions to get the volume and total surface area instantly.
Unlike a sphere, which is fully defined by its radius alone, a cone's size also depends on how tall it is — the same base radius can belong to a short, squat cone or a tall, narrow one, with very different volumes. That's why both Dimension 1 (radius) and Dimension 2 (height) are needed.
The [Area Calculator](/area-calculator/) handles flat, two-dimensional shapes like circles, rectangles, and triangles, measuring area and perimeter. This Volume Calculator handles three-dimensional solid shapes, measuring the space they enclose and the area of their outer surface.
Yes — if you enter dimensions in centimetres, the volume result is in cubic centimetres, which equals millilitres (1 cm³ = 1 mL), so dividing by 1,000 gives you litres. Make sure all three dimensions use the same unit before calculating.
Surface area matters whenever you're covering, painting, or wrapping a 3D object, while volume matters when you're filling it or working out how much material it's made from. Knowing both together is useful for tasks like estimating paint needed for a cylindrical tank or material needed to wrap a box.
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