Volume of Revolution Calculator

Calculate the volume and surface area of a solid of revolution using the disk or shell method.

Function Type

Coefficient a

Coefficient b

x Start

x End

Method

Tab to move between fields

Volume

8.3776 cubic units

Surface Area17.7715 sq units

How to Use This Calculator

Select the function f(x) that will be revolved, and enter its defining parameters.
Set the bounds of integration (a to b) along the x-axis — the solid extends across this interval.
Choose the Disk Method (revolution around x-axis): V = π ∫[a,b] [f(x)]² dx.
Choose the Shell Method (revolution around y-axis): V = 2π ∫[a,b] x·f(x) dx.
The cross-section profile chart shows the radius of the solid at each x value, representing half the disk diameter.
Both methods produce the same volume for the same region — choose based on which integral is easier to set up.

How the result changes with x End

Function Type: Function to revolve around the x-axis
Coefficient a: Leading coefficient
Coefficient b: Second coefficient
x Start: Left bound of rotation region
x End: Right bound of rotation region
Method: Disk method integrates cross-sectional areas; shell method integrates cylindrical shells

Identify Input Parameters
4 parameters
Function Type = 1, Coefficient a = 1, Coefficient b = 0, x Start = 0 = 6 input(s) provided
Calculate Volume
Volume = volume
8.3776 = 8.3776

Engine last updated August 5, 2026. Checked against 3 independently-derived tests — how we verify calculators.

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