Paraboloid Surface Area and Volume Calculator

A paraboloid is a solid of revolution that results from rotating a parabola around its axis of symmetry. If you know the height and radius of a paraboloid, you can compute its volume and surface area with simple geometry formulas. You can also use the calculator on the left.

Volume Formula

If the height of a paraboloid is denoted by h and the radius by r, then the volume is given by the equation

V = (π/2)hr²

Notice that this is less than the volume of a cylinder but more than the volume of a cone with the same dimensions.

Surface Area Formula

The surface area of a paraboloid, not including its base, is given by the formula

SA = (π/6)(r/h²)[(r² + 4h²)^3/2 - r³]

Since the base of the figure has an area of πr², the formula for surface area including the base is

SA_b = (π/6)(r/h²)[(r² + 4h²)^3/2 - r³] + πr²

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