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Volume of Revolution Calculator

Disk, washer and shell methods about the x-axis, the y-axis, or any line y = k or x = k. The integral is set up on screen before it is evaluated, and shifting the axis changes the radius to |f(x) − k| — the step most calculators get wrong.

Related tools

All Geometry tools →
Surface of Revolution CalculatorS = 2π∫ f·√(1+f′²) dx about the x-axis, with the radius and the arc-length element both rederived for the other axes. The sphere case √(1−x²) on [−1, 1] returns exactly 4π despite the integrand blowing up at both endpoints.Aquarium volume calculatorCompute the water volume of a rectangular aquarium in litres and gallons.Cone volume calculatorCompute the volume, surface area and slant height of a cone, drawn to scale.Cylinder volume calculatorCompute the volume and surface area of a cylinder from its radius and height.Pyramid volume calculatorCompute the volume of a square-based pyramid from its base and height.Sphere volume calculatorCompute the volume and surface area of a sphere from its radius.Triangular prism volume calculatorCompute the volume of a triangular prism from its base, height and length.Volume calculatorCompute the volume of a box, cube, sphere, cylinder or cone.

Volume of Revolution Calculator works straight from this page — free, instant, nothing to install. You will find it under Geometry, with Surface of Revolution Calculator and Aquarium volume calculator for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Volume of Revolution Calculator do?

Disk, washer and shell methods about the x-axis, the y-axis, or any line y = k or x = k. The integral is set up on screen before it is evaluated, and shifting the axis changes the radius to |f(x) − k| — the step most calculators get wrong.

When would I actually use this?

Homework and site work alike: how much paint a wall takes, how much water a tank holds, whether a corner is square — and, on the coordinate side, the slope between two points, the distance across a plan, the midpoint of a span.

What is the most common mistake?

Mixing units inside one shape. Entering a length in centimetres and a width in metres gives an area wrong by a factor of a hundred, and the result looks perfectly plausible.

How is Volume of Revolution Calculator different from Surface of Revolution Calculator?

They sit next to each other but answer different questions. Surface of Revolution Calculator: s = 2π∫ f·√(1+f′²) dx about the x-axis, with the radius and the arc-length element both rederived for the other axes. The sphere case √(1−x²) on [−1, 1] returns exactly 4π despite the integrand blowing up at both endpoints. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Aquarium volume calculator is the closest one after this: Compute the water volume of a rectangular aquarium in litres and gallons.

What else is worth having open alongside it?

Cone volume calculator and Cylinder volume calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The formulas are the classical ones and the results are exact to the precision shown — geometry does not change with the year or the country, so nothing here needs updating.

Further reading

All guides →
ExplainerA Cone Is Exactly One Third of Its CylinderRadius 5, height 10: the cone holds 261.8 and the cylinder around it holds 785.4. The ratio is exactly a third, and it holds for any base shape at all.ExplainerTwice as Wide Holds Four Times as Much; Twice as Tall Holds TwiceA cylinder of radius 5 and height 10 holds 785.4 units of volume. Double the radius and it holds 3,141.6; double the height instead and it holds 1,570.8.How-toHow to Calculate VolumeVolume is the space inside a shape. Here's how to find it for boxes, cylinders and spheres, and why keeping your units consistent is the whole game.How-toCircle: Circumference and AreaCircumference is 2πr, area is πr². Here's how radius, diameter and π fit together, both formulas worked through, and how not to mix them up.How-toWhat Wattage of Heater Does an Aquarium Need? Volume Is Only Half the AnswerThe same tank needs a 100 W heater in a warm flat and 300 W in an unheated room. The variable is the gap between the water and the room, which most rules of thumb drop entirely. Plus why two smaller heaters beat one big one, and where this calculator's recommendation stops being trustworthy.ExplainerA Kitchen Scale and a Jug Tell You If That Tap Is Really BrassWeigh it, sink it in water, divide. 340 g displacing 40 cm³ is 8.5 g/cm³ and brass; 272 g in the same 40 cm³ is 6.8 and a zinc casting wearing brass plate.