Semicircle Calculator
From a single radius, get the area, the perimeter, the curved arc length, and the diameter — every number that describes a half circle.
Perimeter includes the flat edge
A semicircle's perimeter is the curved arc plus the straight diameter — not just half a circle's circumference, so don't forget the flat side.
What is a semicircle calculator?
One radius in, the whole half circle out
A semicircle calculator turns one measurement — the radius — into the numbers that describe a half circle: the area, the perimeter (the way around the whole shape), the arc length (just the curved part), and the diameter (the straight edge across the flat side). Each one is fixed once you know the radius, because every circle and half circle shares the same constant π (pi). That makes the single input all you need for arched windows and doorways, half-round mouldings, fan shapes, protractors, race-track ends, and any geometry homework where a half circle shows up.
Enter the radius in any length unit to get the area, perimeter, arc length, and diameter instantly.
A few short formulas, all built from the radius r and the constant π (about 3.14159).
area = ½ × π × r²The area is exactly half a full circle, ½ × π × r². The arc length — the curved edge — is half the circumference, π × r. The diameter, the straight edge across the flat side, is 2 × r. The perimeter is the whole way around, so it adds the curved arc to the straight diameter: π × r + 2 × r.
Suppose your semicircle has a radius of 5.
Arc length and diameter
π × 5 ≈ 15.707963 for the curved edge, and 2 × 5 = 10 across the flat side.
Perimeter
15.707963 + 10 ≈ 25.707963 all the way around — arc plus diameter.
Area
½ × π × 5² = ½ × π × 25 ≈ 39.269908 square units — the space inside.
The four outputs answer different practical questions. The area (about 39.269908 square units for r = 5) is the flat space the half disc covers — the glass in an arched window, the felt for a fan, the paint for a half-round panel. The arc length (about 15.707963) is just the curved edge, the length of trim or LED strip you would bend around the top of an arch. The diameter (10) is the straight bottom edge, the width of the opening. The single most useful insight is that the perimeter (about 25.707963) is the arc plus that straight diameter, not half a circle's circumference — a common mistake is to halve the full circumference and forget the flat edge entirely, which leaves the bottom of the shape open. Because everything scales with the same π, doubling the radius quadruples the area but only doubles the arc and the diameter.
The formulas are exact, but a couple of practical points are worth keeping in mind.
A true half circle, and consistent units
These formulas describe a perfect semicircle — exactly half of a full circle, cut along a diameter. A segment cut along a chord that is not the diameter, a half ellipse, or an arch that is only roughly round will differ from the computed value. The radius is also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: a radius in centimetres gives a perimeter, arc, and diameter in centimetres and an area in square centimetres, never a mix.