Spherical Wedge Volume Calculator
From a sphere radius and a wedge angle in degrees, get the volume of the orange-slice piece of the sphere — the part between two half-planes meeting along the axis.
Radius and angle in, volume out
Enter the sphere radius and the wedge angle in degrees and the calculator returns the wedge volume, (2/3)·R³·α — a 360° wedge gives back the whole sphere.
The angle is degrees, not a length
The wedge angle is measured in degrees (0–360°); only the radius carries a length unit, so the volume comes back in cubic units of that radius unit.
What is a spherical wedge?
The orange-slice piece of a sphere
A spherical wedge — sometimes called a spherical ungula — is the piece of a solid sphere caught between two flat half-planes that meet along a diameter (the sphere's axis), exactly like a single segment of an orange. Two numbers fix it completely: the radius of the whole sphere and the dihedral angle of the wedge, the angle between those two flat faces. Because the wedge is a fixed fraction of the sphere — its angle out of a full turn — its volume is just that fraction of the sphere's volume. That makes it the right tool for orange and melon slices, pie-shaped tank sections, dome segments, and any geometry problem about a fractional sphere.
Enter the sphere radius and the wedge angle in degrees to get the wedge volume instantly — 360° returns the full sphere.
One short formula, built from the radius R, the angle in degrees, and the constant π (about 3.14159).
volume = (2/3) × R³ × α (α in radians)First convert the angle to radians: α = angle × π / 180. Then the volume is (2/3) × R³ × α. This is the sphere's volume (4/3)πR³ scaled by the wedge's share of a full turn — at 360° (α = 2π) the formula collapses to (2/3)·R³·2π = (4/3)πR³, the whole sphere, as it must.
Suppose you have a sphere of radius 5 and want a 90° wedge.
Angle to radians
90 × π / 180 = 1.570796 radians — a quarter turn.
Apply the formula
(2/3) × 5³ × 1.570796 = (2/3) × 125 × 1.570796 = 130.899694 cubic units.
Sanity check
A 90° wedge is a quarter of the sphere; (4/3)π·5³ ≈ 523.598776, and a quarter of that is 130.899694 — they match.
The volume tells you how much solid sphere sits inside the wedge. The most useful intuition is that the wedge is simply a fraction of the whole sphere: its angle divided by 360°. A 90° wedge is a quarter of the sphere, a 180° wedge is a half-sphere, and a 360° wedge is the entire ball — so doubling the angle doubles the volume, while changing the radius scales the volume by the cube of the change (twice the radius means eight times the volume). For r = 5 and a 90° wedge the volume is about 130.899694 cubic units, exactly one quarter of the sphere's 523.598776. Use this for an orange or melon slice, a pie-shaped section of a spherical tank, or a wedge cut from a dome. Keep in mind that the angle drives the answer linearly while the radius drives it cubically, so a small change in radius moves the volume far more than the same change in angle.
The formula is exact, but a couple of practical points are worth keeping in mind.
A true wedge through the centre, angle in degrees
This formula describes a wedge whose two flat faces both pass through the sphere's centre and meet along a diameter — a genuine orange slice. A cut that misses the centre, a spherical cap or sector (sliced by a plane, not two half-planes through the axis), or a flattened or dented ball will differ from the computed value. The angle must be entered in degrees between 0 and 360, and only the radius carries a length unit, so the volume is in cubic units of that same unit.