๐Volume of Revolution Calculator
Find the volume of a solid formed by revolving a region, using the disk, washer, or shell method.
Calculations run entirely in your browser using math.js for parsing and Simpson's rule for the integral. No data is sent to a server.
Free Volume of Revolution Calculator
Trying to find the volume of a solid formed by spinning a region around an axis? Our free volume of revolution calculator sets up and solves it instantly using the disk, washer, or shell method. Enter one or two functions, your interval, and the axis of revolution, and see the correct method auto-suggested, the integral built step by step, and the final volume computed.
When the axis is horizontal, the disk or washer method applies with x-integration; when the axis is vertical, the shell method applies automatically. A shaded graph shows exactly which 2D region is being revolved and around which axis.
Enter your functions and interval to get started. No sign-up, no downloads, no limits โ just clear, worked-out calculus whenever you need it. See the About page or the FAQ for more.
About the Volume of Revolution Calculator
Features
Method auto-suggestion
Disk, washer, or shell chosen from the axis orientation.
Step-by-step setup
The integral formula shown before the final value.
Crossing-curve handling
The integrand automatically uses whichever curve is farther from the axis.
Shaded region graph
Shows the 2D region and axis of revolution.
Frequently Asked Questions
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.