📦 Volume Calculator
Volume
Calculator
The Volume Calculator enables you to calculate the volume of various three-dimensional objects, including cubes, rectangular prisms, cylinders, and spheres. Calculating volume is crucial in various fields, including construction, engineering, packaging, and education. By inputting the necessary measurements, this tool quickly applies the appropriate mathematical formulas to deliver precise results. It removes the need for manual calculations, thereby diminishing the likelihood of mistakes. This resource is particularly beneficial for students studying geometry, professionals dealing with measurements, and anyone requiring quick volume calculations. The calculator is straightforward, quick, and compatible with all devices. The volume results provided are meant for general guidance and estimation; for technical or commercial applications, it is advisable to seek professional confirmation.
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🧮 Volume Calculator – Quick Guide
Functions
| Symbol | Meaning |
|---|---|
| h | Height |
| s | Slant height |
| a | Side length |
| e | Lateral edge length |
| r | Half of side length (r = a / 2) |
| V | Volume |
| L | Lateral surface area |
| B | Base surface area |
| S | Total surface area |
📚 Complete Volume Calculator Guide
This guide explains common 3D shapes along with their volume and surface area formulas. These calculations are widely used in mathematics, engineering, architecture, and education.
🏔 Square Pyramid
A pyramid has a square base and triangular sides.
- Volume:
V = (1/3) × a² × h - Lateral Surface Area:
L = 2a√(a²/4 + h²) - Base Area:
B = a² - Total Surface Area:
S = L + B
🧊 Cube
A cube has six equal square faces.
- Volume:
V = a³ - Lateral Surface Area:
L = 4a² - Base Area:
B = a² - Total Surface Area:
S = 6a²
🍦 Circular Cone
A cone has a circular base that narrows to a point.
- Volume:
V = (1/3)πr²h - Lateral Surface Area:
L = πrl - Base Area:
B = πr² - Total Surface Area:
S = L + B
🏺 Cylinder
A cylinder consists of two circular bases connected by a curved surface.
- Volume:
V = πr²h - Lateral Surface Area:
L = 2πrh - Base Area:
B = πr² - Total Surface Area:
S = L + B
⚪ Sphere
A sphere is a perfectly round 3D object.
- Volume:
V = (4/3)πr³ - Surface Area:
S = 4πr²
🌗 Hemisphere
A hemisphere is half of a sphere.
- Volume:
V = (2/3)πr³ - Curved Surface Area:
L = 2πr² - Base Area:
B = πr² - Total Surface Area:
S = L + B
📦 Rectangular Prism (Cuboid)
A rectangular prism has six rectangular faces.
- Volume:
V = l × w × h - Lateral Surface Area:
L = 2h(l + w) - Base Area:
B = l × w - Total Surface Area:
S = 2(lw + lh + wh)
🔻 Conical Frustum
A frustum is a cone with its top cut off.
- Volume:
V = (1/3)πh(r₁² + r₂² + r₁r₂) - Lateral Surface Area:
L = π(r₁ + r₂)l - Base Area:
B = π(r₁² + r₂²) - Total Surface Area:
S = L + B
💊 Capsule (Cylinder with Hemispherical Ends)
Commonly used in pharmaceutical and industrial designs.
- Volume:
V = πr²h + (4/3)πr³ - Surface Area:
S = 2πrh + 4πr²
🧠 Spherical Cap
A spherical cap is a portion sliced from a sphere.
- Volume:
V = (1/3)πh²(3r − h) - Surface Area:
S = 2πrh