Volume Calculator

Are you looking for a free online calculator that computes the volume of any geometric shape? You are at the right place our handy Volume Calculator will give answers to all your questions in a short span of time. Avail the easy to operate tool to find the volume.


Volume

Volume Calculator tool is helpful to find the volume of circular cone, capsule, circular cylinder, conical frustum, cube, pyramid, hemisphere, rectangular prism, triangular prism, sphere, box and spherical cap. You must select any one of these geometric shape and provide the required input fields. Hit on the volume button to see the exact results easily & quickly. In addition to the instant output, you can also find the formulas and step by step procedure to solve the volume.

What is meant by Volume?

Volume is the quantity of a three dimensional space enclosed by a closed surface. The space that a substance or shape occupies is also called the volume. The SI unit of volume is cubic meter.

Volume Formulas

The formula involved in finding the volume of a shape is not same. It totally depends on the shape of the substance. Get the formulas for various shapes volume in the following sections.

The formula to calculate volume of a Capsule is V = πr²((4/3)r + a)

Circular Cone Volume formula is V = (1/3)πr²h

Conical Frustum Volume is V = (1/3)πh (r₁² + r₂² + (r₁ * r₂))

Circular Cylinder Volume formulas is V = πr²h

Cube Volume formula is V = a3

The formula of Hemisphere Volume is V = (2/3)πr3

Pyramid Volume formula is V = (1/3)a²h

Rectangular Prism volume formula is V = lwh

Sphere Volume formula is V = (4/3)πr3

Spherical Cap Volume formula is V = (1/3)πh²(3R - h)

Triangular Prism Volume formula is V = (1/4)h√[(a + b + c)(b + c -a)(c + a - b)(a + b - c)]

Ellipsoid Volume Formula is V= (4/3)πabc

Volume of a Capsule Formula

Capsule volume, surface area and circumference formulas are given here:

  • Volume of a capsule:
    • = πr²((4/3)r + a)
  • Surface area of a capsule:
    • S = 2πr(2r + a)
  • Circumference of a capsule:
    • C = 2πr

Where,

r is the radius of the circle

a is the side length

Formula to Calculate Circular Cone

Circular cone is a closed figure having circle at the bottom and two lines on the circle joins at one point. Its formulas are here.

  • Volume of a Cone:
    • V = (1/3)πr²h
  • Slant height of a cone:
    • s = √(r² + h²)
  • Lateral surface area of a cone:
    • L = πrs = πr√(r² + h²)
  • Base surface area of a cone:
    • B = πr²
  • Total surface area of a cone:
    • A = L + B = πrs + πr² = πr(s + r) = πr(r + √(r² + h²))

Where,

r is the radius

h is the height

s is slant height of cone

Volume of Conical Frustum Formula

  • Volume of a conical frustum:
    • V = (1/3)πh (r₁² + r₂² + (r₁ * r₂))
  • Slant height of a conical frustum:
    • s = √((r₁ - r₂)² + h²)
  • Lateral surface area of a conical frustum:
    • S = π * (r₁ + r₂) * s = π * (r₁ + r₂) * √((r₁ - r₂)² + h²)
  • Top surface area of a conical frustum (a circle):
    • T = πr₁²
  • Base surface area of a conical frustum (a circle):
    • B = πr₂²
  • Total surface area of a conical frustum:
    • A = π * (r₁² + r₂² + (r₁ + r₂) * s) = π * [ r₁² + r₂² + (r₁ + r₂) * √((r₁ - r₂)² + h²) ]

Where,

r₁ is the radius of circle1

r₂ is the radius of circle2

h is height

s is slant height

Volume of circular cylinder formula

Circular cylinder is having two circles of equal radii one on the bottom one is at the top. Two straight and parallel lines joins those circles. Its formula is

  • Calculate volume of a cylinder:
    • V = πr²h
  • Calculate the lateral surface area of a cylinder:
    • L = 2πrh
  • Calculate the top and bottom surface area of a cylinder:
    • T = B = πr²
  • Total surface area of a closed cylinder is:
    • A = L + T + B = 2πrh + 2(πr²) = 2πr(h+r)

Where,

r is the circle radius

h is the height of cylinder

Volume of Cube formula

Volume of a cube defines the number of cubic units occupied by the cube completely. Cube is a solid three dimensional figure which is having 6 faces.

  • Volume of Cube:
    • V = a3
  • Surface Area of Cube:
    • S = 6a²
  • Volume of Cube From Its Diagonal
    • V = √3 × d3/9

Where,

d is the diagonal of a cube

a is the side length of cube

Volume of Hemisphere Formula

We have different ways to calculate the hemisphere volume based on the available parameters.

  • If you know radius
    • V = (2/3)πr3
  • If you know diameter
    • V = 1/12 * π * d³
  • If you know base area
    • V = 2/3 * √(Ab³ / π)
  • If you know cap area
    • V = 1/3 * √[Ac³ / (2 * π)]
  • If you know total area
    • V = 2/9 * √[A³ / (3 * π)]
  • If you know surface to volume ratio
    • V = 243 * π / (4 * (A/V)³)

Other hemisphere formulas are

  • Diameter of a hemisphere:
    • d = 2 * r
  • Base surface area of a hemisphere:
    • Ab = π * r²
  • Cap surface area of a hemisphere:
    • Ac = 2 * π * r²
  • Total surface area of a hemisphere:
    • A = 3 * π * r²
  • Surface to volume ratio of a hemisphere:
    • A / V = 9 / (2 * r)

Where,

r is the radius

d is the diameter

Ab is the base area

Ac is the cap area

A is the total area

Volume of Pyramid Formula

The three main parts of the pyramid are apex, face and base. The base of pyramid will be any geometrical shape, face is the isosceles triangles and all those triangles meet at the top of the pyramid called apex.

  • Pyramid Volume:
    • V = (1/3)a²h
  • Base area of pyramid:
    • A = a²
  • Surface Area of a pyramid:
    • S = 2as + a²

Where,

a is the side length of base

s is the slant height

h is the height of a pyramid

Volume of Rectangular Prism Formula

Rectangular prism is a three dimensional figure having 4 rectangular phases and 2 square phases.

  • Volume of Rectangular Prism:
    • V = lwh
  • Surface Area of Rectangular Prism:
    • S = 2(lw + lh + wh)
  • Space Diagonal of Rectangular Prism:
    • d = √(l² + w² + h²)

Where,

l is the length of the prism

w is the width of the prism

h is the height of prism

Volume of Sphere Formula

A symmetrical 3 dimensional circular shaped object is called sphere. Its volume, surface area formulas are given here:

  • Sphere Volume:
    • V = (4/3)πr3
  • Diameter of a Sphere:
    • D = 2r
  • Surface Area of Sphere:
    • A = 4πr²

Where:

r is the radius

D is diameter

A is surface area

V is volume

Volume of Spherical Cap Formula

Spherical cap is the region of a sphere which lies below or above the plane. Formulas are

  • Spherical Cap Volume:
    • V = (1/3)πh²(3R - h)
  • Surface Area of Spherical Cap:
    • S = 2πRh

Where,

R is the radius

h is the height

Volume of Triangular Prism Formula

A prism which has 3 rectangular faces & 2 parallel triangular bases is known as triangular prism.

  • Volume of Triangular Prism:
    • V = (1/4)h√[(a + b + c)(b + c -a)(c + a - b)(a + b - c)]
  • Surface Area of a Triangular Prism:
    • S = ab + 3bh

Where,

a, b, c are sides of a triangle

h is the height of triangle

Volume of Ellipsoid Formula

  • Ellipsoid Volume:
    • = (4/3)πabc
  • Surface Area of Ellipsoid:
    • S ≈ 4π(((ab)1.6 +(ac)1.6 + (bc)1.6)/3)1/1.6

Where,

a, b, c are the axis of the ellipsoid

V is volume

S is surface area

How to Calculate Volume?

You can follow the simple steps offered below to calculate the volume of any three dimensional geometrical shape Or use our free Volume Calculator Tool.

  • Get the data about that particular shape from the table.
  • Substitute those values in the given formulas.
  • Perform all required math operations to get the result.

You can get the information regarding geometry concepts on our site Areavolumecalculator.com