What is a sphere calculator?
A sphere calculator computes the volume, surface area, and diameter of a sphere from a single input: the radius. A sphere is a perfectly round 3D shape—every point on its surface is the same distance from the center. You enter the radius (the distance from the center to the surface); the calculator gives you volume = (4/3)πr³, surface area = 4πr², and diameter = 2r. No sign-up or download is required; the tool runs in your browser and is useful for geometry, physics, and any task involving spherical shapes.
Spheres appear in balls, planets, bubbles, and many natural and manufactured objects. Knowing the volume helps with capacity and displacement; surface area helps with coating, paint, or heat transfer. This free sphere calculator gives you volume in cubic units and surface area in square units—meters, feet, inches—as long as you use the same unit for radius. The diameter is twice the radius and is often used in specifications.
How to use this sphere calculator
Enter the radius of your sphere in the input box. The radius must be a positive number—the distance from the center to any point on the surface. You can use decimals (e.g. 2.5) or whole numbers (e.g. 2). As soon as the radius is valid, the results appear: volume in cubic units, surface area in square units, and diameter in the same linear unit as the radius. The formulas are shown under the input: volume = (4/3)πr³, surface area = 4πr², diameter = 2r. If you enter zero or a negative value, the calculator will ask you to enter a positive radius. If you only know the diameter, divide it by 2 to get the radius and enter that.
Sphere volume formula
The volume of a sphere is V = (4/3)πr³, where r is the radius. So the volume is four-thirds of π times the cube of the radius. For example, if the radius is 2 units, volume = (4/3) × π × 8 ≈ 33.51 cubic units. The formula comes from calculus (integrating circular cross-sections) or from the fact that the volume of a sphere is 2/3 of the volume of a circumscribed cylinder (same radius, height 2r). The sphere calculator applies this formula so you get an accurate volume without doing the arithmetic by hand. Volume is always in cubic units when the radius is in a linear unit.
Surface area of a sphere
The surface area of a sphere is A = 4πr². So it is four times the area of a circle with the same radius (πr²). For radius 2, surface area = 4 × π × 4 ≈ 50.27 square units. There is no “base” or “top”—the entire surface is curved. Use surface area when you need to paint a ball, coat a sphere, or estimate heat loss or exposure. The sphere calculator gives you both volume and surface area from the same radius. Interestingly, the derivative of the volume formula (4/3πr³) with respect to r is 4πr², the surface area; this relationship holds for spheres and is useful in calculus.
Radius and diameter
The radius is the distance from the center of the sphere to any point on its surface. The diameter is twice the radius—the longest distance across the sphere, passing through the center. Many real-world specs use diameter (e.g. ball size, planet size). This calculator gives you the diameter whenever you enter the radius. If you only know the diameter, divide it by 2 and enter that as the radius. All three outputs—volume, surface area, and diameter—are derived from the same radius, so one input gives you everything.
Sphere vs circle and other solids
A circle is a 2D shape; a sphere is its 3D analogue. The circle’s area is πr²; the sphere’s surface area is 4πr² (four times the area of a great circle). The sphere’s volume is (4/3)πr³. A cylinder that circumscribes a sphere (radius r, height 2r) has volume 2πr³ and surface area 6πr²; the sphere has two-thirds of that volume and two-thirds of the cylinder’s curved surface area. This sphere calculator focuses on the sphere; enter the radius to get volume, surface area, and diameter. For circles, cylinders, or cones, use their dedicated calculators.
Applications of sphere calculations
Sphere volume and surface area are used in many fields. In physics and engineering, spheres model particles, droplets, and planets; volume relates to mass and density, surface area to drag or heat transfer. In sports, ball sizes are often given by diameter or circumference. In chemistry and biology, cell or bubble sizes are sometimes spherical. In education, the sphere is a standard solid when studying volume and surface area. This sphere calculator gives you quick, accurate results from the radius. Always measure radius (or diameter/2) in the same units you want for volume (cubic) and surface area (square).
Summary
This sphere calculator finds the volume, surface area, and diameter of a sphere from the radius. Enter the radius (a positive number) and get volume = (4/3)πr³, surface area = 4πr², and diameter = 2r instantly. The tool is free, runs in the browser, and requires no account. Use it for homework, design, or any spherical shape. If you know the diameter, use half of it as the radius. Keep units consistent for accurate results.