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.
Formula: V = 4/3 π r³
Formula: V = 1/3 π r² h
Formula: V = a³
Formula: V = π r² h
Formula: V = l × w × h
Formula: V = π r² (4/3 r + h)
Formula: V = 1/3 π h² (3R - h) = 1/6 π h (3r² + h²)
Enter any 2 values to solve the cap.
Formula: V = 1/3 π h (r² + rR + R²)
Formula: V = 4/3 π a b c
Formula: V = 1/3 a² h
Formula: V = π l / 4 (d₁² - d₂²)
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.
The SI unit of volume is the cubic meter (m³). By definition:
Rotating a curve y = f(x) about the x-axis integrates infinitesimal circular disks of area π y²:
The volume of any irregularly shaped solid submerged in a fluid equals the volume of fluid displaced:
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.
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.
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.
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.