The Volume and Surface Area Calculator is an easy-to-use online tool that helps you compute two of the most important properties of 3D shapes: their volume (the amount of space they occupy) and their surface area (the total area covering the outer surface of the shape). It’s designed for everyday users, students, teachers, engineers, architects, and anyone who works with measurements or geometry.
Instead of memorizing complex mathematical formulas for each individual shape, this calculator allows you to select a shape from a visual list, input the required dimensions (like radius, height, or side length), and instantly get the accurate results. It's perfect for quick calculations, educational use, or even for checking your own work.
The tool supports a wide variety of geometric shapes, including common ones like cubes, cylinders, cones, and spheres, as well as more advanced shapes such as toruses, frustums, and spherical zones. Each shape has its own set of required measurements, and the calculator only asks for the specific values needed for that shape — nothing more, nothing less.
Once you've selected a shape and entered the values, the calculator will display the results in real-time, including:
To make things even easier, the calculator shows a helpful image of the selected shape along with labeled parts, so you know exactly which measurements to enter. You can even toggle between alternative methods — for example, entering either the side length or slant height, depending on what data you have available.
Whether you're doing homework, designing a container, planning a construction project, or just satisfying your curiosity, the Volume and Surface Area Calculator is here to save you time, reduce error, and make geometry simple and accessible for everyone.
Using the Volume and Surface Area Calculator is quick and easy. Just follow these three simple steps:
Start by choosing the 3D shape you want to work with. You’ll find a list of shapes such as Cone, Cylinder, Sphere, Cube, and many others. Simply click the radio button next to your desired shape, and an image will appear to help you visualize it.
Once you've selected a shape, a set of input fields will appear. These fields will ask for specific measurements like radius, height, diameter, or side length — depending on the shape. Make sure to enter numbers only. Some shapes give you options, like choosing between radius or circumference, so you can use whichever measurement you have available.
After entering all the necessary values, click the “Calculate” button. The calculator will instantly display the results, including volume, surface area, and other relevant information like slant height or center of gravity when applicable.
The calculator supports a wide range of 3D shapes. Each one comes with its own image and specific input fields based on its geometry. Below is the list of all available shapes you can choose from:
Each shape includes the exact fields needed for accurate volume and surface area calculation. Simply select one to begin!
Each shape in the calculator requires specific values to compute its volume and surface area. Below is a guide to help you understand which measurements you’ll need to provide and what they represent. In some cases, you’ll have options — like entering either radius or circumference — depending on the data you have.
Always enter values using consistent units (e.g., cm, m, in), and make sure to input numbers only. If a value is missing or invalid, the calculator may not show a result.
After entering your values and clicking "Calculate," the calculator will show several results depending on the shape you selected. Here's what each result means:
All results are shown with up to three decimal places for accuracy. You can use them for construction planning, volume estimation, material calculations, and much more.
To make the calculator easier to use, a helpful image appears every time you select a shape. These visuals are designed to clearly show the shape and its parts — such as height, radius, base, slant height, and other key measurements — so you know exactly what values to enter.
For example:
These diagrams serve as quick references, especially if you're unfamiliar with geometric terms. They help prevent errors by showing exactly where each dimension should be measured.
As soon as you select a different shape, the corresponding image updates automatically — giving you a visual guide to match the input fields shown.
To ensure accurate results and a smooth experience, keep the following tips and warnings in mind when using the calculator:
By following these tips, you’ll get more accurate results and avoid common mistakes.
If no result appears after clicking "Calculate," make sure you’ve entered all the required values for the selected shape. Double-check that the inputs are valid numbers and that you haven’t left any fields empty. Some shapes also offer alternative inputs — use only one method, not both.
Yes, you can! The calculator accepts both whole numbers and decimals. Just use a dot (.) for the decimal point, for example: 7.5 or 12.3.
You can use any unit you prefer (e.g., centimeters, meters, inches), but it’s important to use the same unit for all inputs in a single calculation. The results will be in cubic units for volume and square units for surface area, based on the unit you use.
No installation is needed. The calculator runs directly in your web browser — just open the page and start using it.
If you enter a wrong value, you can simply change it or clear the input field. You can also select a different shape and start over — the calculator will automatically reset the form for the new shape.
Yes! The calculator is designed to work on all devices — phones, tablets, and computers. The layout adjusts automatically for smaller screens.
Some shapes allow alternative inputs. For example, in spherical caps or hexagonal prisms, you can use either radius or chord/side/slant. If you’re unsure which one to use, refer to the image shown for that shape.
Although it is entirely composed of a single curved surface, it is possible to calculate the area of the sphere.
A = 4 . π . r² where r = measure of the radius
From its curved surface, we can see a certain resemblance between this formula and that allowing to calculate the area of a disc. Thus, only one measurement is essential to allow the use of this formula, namely the measurement of the radius.
The volume of a Sphere corresponds to the space inside the sphere which delimits it. To find its volume, just apply this formula:
V = 4 . π .r3 with r = measure of the radius
Once again, only the radius measurement is necessary to complete the process.
The volume delimited by a spherical cap of height h and the sphere of radius r is:
V = π .r2 (r - h/3)
The volume V of a spherical sector corresponding to a spherical cap of height h in a ball of radius r is given by the relationship:
V = (2 . π .r2 .h)/3
The area of a spherical zone or of a spherical cap is given by the following formula:
A = 2π .r .h
in which :
r is the radius of the sphere;
h is the distance between the two parallel planes.
The volume V of a spherical Zone corresponding to a spherical cap of height h in a ball of radius r is given by the relationship:
V = π h / 6 (3R2 + 3r2 + h2)
in which :
h: height of the zone
a: large radius
b: small radius
Johannes KEPLER (German mathematician and astronomer, 1571-1630) established the following formula to calculate an approximate value V of the volume of a barrel:
Barrel Volume =(πh/12) x (2D2 + d2)
h: height
D: middle radius
d: top & bottom radius
The area A of a torus of radius R generated by a disk of radius r is given by:
A = 4π2 . R . r
in which :
R: large radius
r: small radius
The volume V of a torus of radius R generated by a disk of radius r is given by:
V = 2π2 . r2 . R
in which :
R: large radius
r: small radius