Volume of Hemisphere Calculator
Compute hemisphere volume from radius, diameter, surface areas, surface-to-volume ratio, or volume itself. Choose a parameter, set units, get steps.
Equation Preview
Helping Notes
- Formulas (hemisphere): V = (2/3)πr³; d = 2r; A_b = πr²; A_c = 2πr²; A = 3πr²; A/V = 9/(2r).
- From diameter: V = (π d³)/12. From A_b, A_c, A: first get r via the definitions above, then compute V.
- Surface-to-volume ratio given: r = 9/(2·(A/V)). Then compute all remaining properties.
- Units are converted internally to SI (m, m², m³) and results are shown with helpful unit conversions.
Results
Hemisphere Volume
Radius & Diameter
Surface Areas
Surface-to-Volume Ratio
Error
Steps
What is Volume of Hemisphere Calculator?
A Volume of Hemisphere Calculator determines the volume enclosed by a half of a sphere (a hemisphere). If a full sphere of radius \(r\) has volume \(\tfrac{4}{3}\pi r^3\), then a hemisphere—being exactly half—has volume \(\tfrac{2}{3}\pi r^3\). The same result may be expressed in terms of diameter \(d=2r\) as \(\tfrac{\pi d^3}{12}\). This tool automates these computations, eliminates arithmetic slips, and explains each substitution, rearrangement, and unit handling step. It’s helpful for tank sizing, domes, lenses, culinary molds, and any geometry or engineering task involving half‑spherical shapes.
About the Volume of Hemisphere Calculator
The calculator accepts radius or diameter in any length units (mm, cm, m, in, ft) and returns the hemisphere volume in both cubic input units and optional conversions (e.g., liters, gallons). It displays responsive, line‑by‑line formulas—defining \(r\) from \(d\) when needed, substituting numerical values, simplifying powers, and multiplying by \(\pi\). For documentation, it labels every step and rounds results to your chosen precision while also offering an exact \(\pi\) form. Advanced options include density‑based mass (multiply by material density) and curved surface area for material estimates.
How to Use this Volume of Hemisphere Calculator
- Select input type: radius \((r)\) or diameter \((d)\).
- Enter the value and choose units; optionally set output precision and a secondary unit (e.g., liters).
- Click calculate to evaluate \(V=\tfrac{2}{3}\pi r^3\) or \(V=\tfrac{\pi d^3}{12}\).
- Review the responsive formula block showing substitution, simplification, and numerical evaluation.
- Copy the exact and decimal results for homework, design specs, or purchasing materials.
Examples
Example 1: Given radius
\(r=5\,\text{cm}\).
Example 2: Given diameter
\(d=10\,\text{m}\Rightarrow r=5\,\text{m}\).
Example 3: Convert to liters
\(r=0.30\,\text{m}\).
FAQs
What is the hemisphere volume formula?
\(V=\tfrac{2}{3}\pi r^3\), or equivalently \(V=\tfrac{\pi d^3}{12}\) using diameter \(d=2r\).
Which units can I use?
Any consistent length unit works; outputs include cubic units and optional conversions like liters or gallons.
Is surface area included?
Curved area \(A_c=2\pi r^2\) is shown as a companion value; including the base disk gives \(A=3\pi r^2\).
How precise are results?
You can select decimal places; an exact form with \(\pi\) is also provided for symbolic work.
Can I compute mass from volume?
Yes—multiply volume by density \(\rho\) to get mass: \(m=\rho V\).
Does the formula change for hollow domes?
Use the difference of two hemisphere volumes: \(V=\tfrac{2}{3}\pi(r_o^3-r_i^3)\).
What if I only know circumference?
Find radius from \(C=2\pi r\), then use the hemisphere volume formula.
Can I enter mixed units?
Avoid mixing (e.g., cm and m). Convert first to keep calculations consistent and correct.
Is this formula valid for partial fills?
Partial fills require spherical cap formulas; this calculator focuses on exactly half of a sphere.