Volume Calculator
Calculate volume calculator for engineering 3d shapes. Accurate physical formulas and verified engineering metrics for engineers, students & technicians.
Calculate Volume Calculator
Enter your engineering parameters below to compute verified physical and mathematical metrics.
Calculation Results
Calculated using verified physical methodology: Cylinder: V = pi*r^2*h | Box: V = l*w*h | Sphere: V = (4/3)*pi*r^3 | Cone: V = (1/3)*pi*r^2*h
Quick Summary
The Volume Calculator computes 3D volumetric displacement, interior liquid capacity, and total surface area across common engineering geometries including cylinders, tanks, rectangular vessels, spheres, and conical hoppers.
How to Use the Volume Calculator
Enter the primary dimension (radius or length), secondary dimension (height or width), depth (for rectangular boxes), and geometry type (1=Cylinder, 2=Box, 3=Sphere, 4=Cone). Click Calculate to view volume across SI and US imperial units.
- Enter Primary Dimension (Radius / Length in meters).
- Enter Secondary Dimension (Height / Width in meters).
- Enter Depth / Thickness (meters - for rectangular prisms).
- Enter Geometric Geometry Type (1=Cylinder, 2=Box, 3=Sphere, 4=Cone).
- Click Calculate to instantly view computed engineering metrics and unit conversions.
Volume Calculator Formula & Method
The mathematical relationships governing this calculator are based on fundamental engineering mechanics:
Cylinder: V = pi*r^2*h | Box: V = l*w*h | Sphere: V = (4/3)*pi*r^3 | Cone: V = (1/3)*pi*r^2*h
Worked Example
For a cylindrical tank with radius r = 0.5 m and height h = 2.0 m: Volume V = pi * 0.5^2 * 2.0 = 1.5708 m³ = 1,570.8 Liters (414.95 US Gallons, 55.47 ft³).
Scope: What is Included vs. Excluded
Included Features
Multi-geometry volume formulas, liquid capacity in Liters and Gallons, cubic feet, cubic yards, and total surface area.
Excluded Factors
Wall thickness deduction unless inner dimensions are directly entered.
Engineering Tips & Best Practices
For pipe or hollow cylinder liquid capacities, use the inner radius (ID / 2) rather than outer diameter.
Common Mistakes to Avoid
Mixing units such as millimeters with meters without prior dimensional conversion.
Frequently Asked Questions
How many Liters are in one cubic meter (1 m³)?
Exactly 1,000 Liters equal 1 cubic meter (1 m³).
How do you calculate the liquid capacity of a horizontal cylinder tank?
For full tanks, capacity is pi*r^2*L. For partially filled tanks, integrate the circular segment area multiplied by cylinder length.
How many US Gallons are in a cubic meter?
1 cubic meter equals approximately 264.172 US liquid gallons.
What is the surface area formula for a cylinder?
Total Surface Area = 2*pi*r*h + 2*pi*r^2 (lateral surface plus top and bottom circular bases).
Can this calculator compute conical hopper storage capacity?
Yes, select geometry type 4 (Cone) to calculate conical hopper volumes: V = (1/3)*pi*r^2*h.