Frequently Asked Questions
Everything you need to know about the Volume of Revolution Calculator.
How does the volume of revolution calculator work?
Enter one or two functions, an interval, and an axis, and it sets up and solves the volume integral instantly with steps shown.
What's the difference between the disk, washer, and shell methods?
Disk is for a single curve revolved about the axis it touches; washer is for the region between two curves; shell is used when revolving about a perpendicular axis. The calculator auto-suggests the right one.
Is it free?
Completely free, no sign-up, downloads, or limits.
Can I override the auto-suggested method?
The method is determined by whether the axis is horizontal or vertical, and is shown clearly with each result.
What if the curves cross within my interval?
The integrand automatically uses whichever curve is farther from the axis at each x, so crossing curves are handled without manual splitting.
What if the integral has no closed form?
It falls back to numerical integration and clearly labels the result as an approximation.
Does it show the region being revolved?
Yes, a shaded graph shows the 2D region and the axis of revolution.
Are results exact or decimal?
Clean results are shown as multiples of ฯ; otherwise decimals are used.
Is my input stored anywhere?
No; everything runs in your browser and isn't stored or sent anywhere.
Does it work on mobile?
Yes, fully responsive, including the graph and step-by-step panel.