Hemisphere Volume Calculator
Calculate hemisphere volume from radius or diameter. See capacity in liters, US gallons, and cups. Perfect for domes, bowls, and tanks.
Rearrange V = (2/3)πr³ to solve for the radius of the dome or bowl.
The volume of a hemisphere is exactly half of a full sphere: V = (2/3) × π × r³. For example, a 10-inch diameter mixing bowl (radius 5 inches) has a volume of 261.80 cubic inches (1.13 US gallons or 4.53 quarts).
Hemisphere Volume Calculator Formula
| Variable | Definition | Standard Units |
|---|---|---|
| V | Internal capacity of the hemisphere | in³, ft³, gal, L, cups |
| r | Radius from center to rim edge | in, ft, cm, or m |
| d | Rim diameter (2 × r) | in, ft, cm, or m |
Hemisphere Formula and Practical Uses
A hemisphere is formed by cutting a full sphere exactly in half through its center. Because a full sphere has volume (4/3)πr³, half of it is (1/2) × (4/3)πr³ = (2/3)πr³. Common examples include mixing bowls, igloos, geodesic dome greenhouses, planetarium ceilings, and spherical tank end caps.
Common Calculation Mistakes to Avoid
- Using the full sphere formula ((4/3)πr³) without dividing by 2
- Using diameter instead of radius in the r³ term
- Confusing the curved dome area (2πr²) with the total area including the circular floor (3πr²)
Frequently Asked Questions
What is the formula for the volume of a hemisphere?▼
How do you find the capacity of a hemisphere bowl?▼
What is the curved surface area of a hemisphere?▼
How many cups or quarts fit in a hemispherical bowl?▼
Authoritative Sources & Reference Standards
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811 — National Institute of Standards and Technology (NIST). Verified 2026-10-01.
Official SI unit definitions, conversion factors (Appendix B), and precision standards for cubic meters, liters, and US customary units.
- Common Core State Standards for Mathematics: High School Geometry (Geometric Measurement and Dimension HSG.GMD.A.1–3) — National Governors Association Center for Best Practices & Council of Chief State School Officers. Verified 2026-10-01.
Curricular standards for volume formulas of cylinders, pyramids, cones, and spheres, including Cavalieri’s principle.