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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.

Related tools

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Volume of Revolution CalculatorDisk, 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.Surface Area CalculatorTotal surface area of a sphere, cylinder, cone, cuboid, prism, pyramid or tetrahedron.Cone surface area calculatorCompute the total surface area and slant height of a cone from its radius and height.Surface gravity calculatorCompute the surface gravity of a planet or moon from its mass and radius.Surface Integral CalculatorCompute scalar (∬ f dS) and flux (∬ F·dS) surface integrals over a parametrized surface.3D Distance CalculatorCompute the distance between two points in space, with an isometric view, the Δx / Δy / Δz components and the midpoint.Angle Bisector Calculator (triangle)Enter the three sides or the three vertices and get the length of each internal angle bisector, the incenter, the inradius, and the exact point where every bisector cuts the opposite side. The angle bisector theorem is the heart of it: the bisector splits the opposite side in the ratio of the two adjacent sides. The triangle inequality is checked before anything is computed, and the triangle is drawn with its three bisectors.Circumscribed Circle CalculatorCircumradius R = abc/4K, circumcentre and circumcircle of a triangle, from three sides or three vertices, with the figure drawn.

Surface of Revolution Calculator is free to use as often as you like, directly from this page. Its place is under Geometry; Volume of Revolution Calculator and Surface Area Calculator answer the questions closest to this one.

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 is 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.

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 Surface of Revolution Calculator different from Volume of Revolution Calculator?

They sit next to each other but answer different questions: Volume of Revolution Calculator is the one to open when you need it to 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. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Surface Area Calculator is the closest one after this: Total surface area of a sphere, cylinder, cone, cuboid, prism, pyramid or tetrahedron.

What else is worth having open alongside it?

Cone surface area calculator and Surface gravity 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 →
ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.ExplainerThe Pythagorean Theorem ExplainedIn a right triangle, a² + b² = c². Here's what the formula means, a worked example, how to find any side, and where it's used in real life.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-toHow to Calculate the Square Metres of a RoomFind a room's area by multiplying length by width. Here's the method for rectangular, L-shaped and round rooms, and why area drives your material orders.