How do you calculate the volume of a cylinder?

The volume of a cylinder is pi times the radius squared times the height: V = pi r squared h. The total surface area includes the two circular ends plus the curved lateral surface: SA = 2 pi r squared + 2 pi r h.

What is the formula for the volume of a cone?

The volume of a cone is one third of pi times the radius squared times the height: V = (1/3) pi r squared h. A cone has exactly one third the volume of a cylinder with the same base and height.

How is the surface area of a sphere calculated?

The surface area of a sphere is 4 times pi times the radius squared: SA = 4 pi r squared. The volume is (4/3) pi r cubed.

Volume Calculator

This volume calculator finds the volume and surface area of six common three-dimensional solids: cube, sphere, cylinder, cone, rectangular prism, and pyramid. Volume is the amount of three-dimensional space a solid occupies, and surface area is the total area of all its outer faces or surfaces. Both measurements appear in engineering, manufacturing, architecture, and everyday tasks such as estimating how much water a tank holds or how much paint a surface needs. Each solid has its own set of formulas derived from the shape's geometry. For a cylinder you need the radius and height; for a cone the radius and height; for a sphere just the radius; for a cube just the edge length; for a rectangular prism the three edge dimensions; and for a pyramid the base length, base width, and height. Select the shape from the dropdown, enter the dimensions in any consistent unit, and the calculator returns the volume in cubic units and the surface area in square units of the same measure. The default example is a cylinder with radius 5 and height 10, giving a volume of 785.40 cubic units and a total surface area of 471.24 square units. This tool suits students working through solid geometry, builders estimating concrete volumes, and tradespeople calculating tank capacities or material quantities. Results are for reference only.

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Shape

Radius

Height

Edge length

Radius

Height

Length

Width

Height

Base length

Base width

Height

785.40

volume (cubic units)

Surface area471.24

ShapeCylinder

How it works

Select your solid and the relevant inputs appear. Formulas: Cylinder V = πr²h, SA = 2πr² + 2πrh. Cube V = s³, SA = 6s². Sphere V = (4/3)πr³, SA = 4πr². Cone V = (1/3)πr²h, SA = πr² + πr√(r²+h²). Rectangular Prism V = lwh, SA = 2(lw+lh+wh). Pyramid V = (1/3)lwh, SA = lw + l√((w/2)²+h²) + w√((l/2)²+h²) (rectangular base approximation for the lateral faces).

Worked example

Cylinder with radius=5 and height=10 (the default): V = π × 25 × 10 = 785.40 cubic units. SA = 2π × 25 + 2π × 5 × 10 = 157.08 + 314.16 = 471.24 square units. Switching to a sphere with radius=5 gives V = (4/3)π × 125 = 523.60 cubic units and SA = 4π × 25 = 314.16 square units.

Related calculators

Area Calculator: compute 2D cross-sectional areas for circles, rectangles and other shapes.
Triangle Calculator: solve any triangle, useful for working out pyramid face areas.
Hypotenuse Calculator: find slant heights needed for cone and pyramid surface areas.
Percentage Calculator: express one volume as a percentage of another for fill or capacity problems.

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