Calculators
Spherical Wedge Calculator
Calculate spherical wedge volume, curved lune area, and total closed surface area from sphere radius and wedge angle.
Measure an orange-segment-shaped portion of a sphere.
A spherical wedge is the solid between two radial half-planes meeting along a sphere diameter. Enter radius R and the interior wedge angle θ in degrees. Convert to radians α = θπ/180. Volume V = 2αR³/3; curved spherical lune area A = 2αR². The two flat semicircular cut faces have combined area πR², so total closed surface area is 2αR² + πR². The fraction of sphere volume is θ/360. For R = 3 and θ = 90°, volume is 9π ≈ 28.2743338823 cubic units, curved area is 9π square units, and total area is 18π ≈ 56.5486677646 square units. A 180° wedge is a hemisphere. Angles above 180° describe the larger wedge. The endpoints 0° and 360° are excluded because their cut faces collapse or disappear. Use radius from 1e-50 to 1e50 and angles from 0.000001 to 359.999999 degrees. Scientific notation is accepted; results use browser floating-point arithmetic rounded to 12 significant digits. This is a solid volume calculator; a lune is only the curved surface. All inputs stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is the difference between a spherical wedge and a lune?
A wedge is a three-dimensional solid. A lune is its curved patch on the sphere. This calculator reports wedge volume, lune area, and closed surface area including both flat cut faces.
Which formulas are used?
With angle α in radians, volume is 2αR³/3 and curved area is 2αR². The two semicircular cut faces add πR² to the closed surface area.
Can I calculate a hemisphere or a larger wedge?
Yes. Use 180 degrees for a hemisphere or an angle above 180 degrees for the larger wedge. Angles must be from 0.000001 to 359.999999 degrees; zero and a full turn have different boundary geometry and are excluded.
What units and input formats can I use?
Use any consistent length unit for radius, including scientific notation from 1e-50 to 1e50. Enter the angle in degrees. Areas use squared length units and volumes use cubed length units. Calculations run locally in your browser.