Volume Calculator
Calculate the volume of 3D geometric shapes: Sphere, Cylinder, Cube, Rectangular Prism, Cone, and Pyramid.
Volume Calculator
Calculate the exact volume and liquid capacity of 11 three-dimensional shapes with automatic metric and imperial unit conversions, wireframe diagrams, and step-by-step formulas.
1Sphere Volume Calculator
Formula: V = 4/3 π r³
2Cone Volume Calculator
Formula: V = 1/3 π r² h
3Cube Volume Calculator
Formula: V = a³
4Cylinder Volume Calculator
Formula: V = π r² h
5Rectangular Tank / Prism Volume Calculator
Formula: V = l × w × h
6Capsule Volume Calculator
Formula: V = π r² (4/3 r + h)
7Spherical Cap Volume Calculator
Formula: V = 1/3 π h² (3R - h) = 1/6 π h (3r² + h²)
Enter any 2 values to solve the cap.
8Conical Frustum Volume Calculator
Formula: V = 1/3 π h (r² + rR + R²)
9Ellipsoid Volume Calculator
Formula: V = 4/3 π a b c
10Square Pyramid Volume Calculator
Formula: V = 1/3 a² h
11Tube / Hollow Cylinder Volume Calculator
Formula: V = π l / 4 (d₁² - d₂²)
Comprehensive Guide to Volume, 3D Geometry & Liquid Capacity
Volume is the quantity of three-dimensional space enclosed by a closed boundary or surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.
SI Unit & Capacity Relationships
The SI unit of volume is the cubic meter (m³). By definition:
Volume Derivations & Calculus of Solids of Revolution
The Disk Integration Method
Rotating a curve y = f(x) about the x-axis integrates infinitesimal circular disks of area π y²:
Archimedes' Fluid Displacement
The volume of any irregularly shaped solid submerged in a fluid equals the volume of fluid displaced:
Frequently Asked Questions
How do you calculate the volume of a hollow cylinder or pipe?
Subtract the volume of the inner void cylinder from the outer solid cylinder: V = π l / 4 × (d₁² - d₂²), where d₁ is the outer diameter, d₂ is the inner diameter, and l is the pipe length.
What is the difference between volume and capacity?
Volume refers to the amount of three-dimensional space a solid object occupies, measured in cubic units (m³, ft³). Capacity refers to the maximum volume of liquid or gas a container can hold, typically measured in liters, milliliters, or gallons.
How do you convert cubic meters to US gallons?
Multiply the volume in cubic meters by 264.172. For example, a 10 m³ swimming pool holds approximately 2,641.72 US gallons of water.
What is a conical frustum?
A conical frustum is the solid portion of a cone that lies between two parallel planes cutting across it perpendicular to its central axis. It resembles a truncated cone or bucket.
Understanding Volume Calculator & Formula
The Volume Calculator on CalculatorScale.com is engineered to deliver instant, mathematically verified calculations conforming strictly to standard institutional equations. Whether planning long-term investments, managing household budgets, tracking clinical fitness targets, analyzing academic genetics, calculating veterinary dosages, or converting dimensional units, every calculation updates dynamically in real time without lag.
Every formula used in this tool adheres to certified international standards, including World Health Organization biometric metrics, veterinary clinical guidelines, NIST physical conversion constants, and standard biological equations. Results are computed entirely client-side inside your browser with complete data privacy, ensuring your sensitive numbers and statistics never leave your device.
Our calculators are 100% free with no registration, subscriptions, or paywalls required. You can toggle between imperial and metric units, customize input parameters, export calculation summaries, or embed this calculator directly into your own website or blog.
How to Use the Volume Calculator
- 1 Select the 3D geometric solid: Cube, Rectangular Prism, Cylinder, Cone, Sphere, Capsule, or Pyramid.
- 2 Enter the required dimensions and select your unit of measurement (inches, feet, cm, meters, yards).
- 3 View the calculated 3D volume in cubic units, along with instant liquid volume conversions (gallons, liters, fluid ounces, milliliters).
Volume Calculator — Frequently Asked Questions
Q1 What 3D geometric shapes can this volume calculator compute? ▾
It calculates the volume of spheres, cylinders, rectangular prisms (cubes/boxes), cones, pyramids, ellipsoids, and capsules.
Q2 What is the formula for the volume of a cylinder and a sphere? ▾
Cylinder volume is V = π·r²·h (where r is radius and h is height). Sphere volume is V = (4/3)·π·r³.
Q3 How do you convert between cubic inches, cubic feet, liters, and gallons? ▾
1 cubic foot = 1,728 cubic inches = 28.3168 liters = 7.48052 US liquid gallons. 1 cubic meter = 1,000 liters = 35.3147 cubic feet.
Q4 How do you measure the volume of an irregular object? ▾
The volume of an irregular object can be measured using Archimedes' water displacement method: submerge the object in water and measure the volume of liquid displaced.
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