Free · Circle calculators ⭕

Half-Disk Area, Diameter and Complete Perimeter

Yes. The full half-disk boundary is πr+2r. The curved semicircle by itself is only πr.

  • Formula & worked example
  • Private in your browser
  • No signup
Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Example in initial displayed units: Radius (r) 4 gives Diameter (d) 8, Area (A) 25.13274, Full boundary perimeter 20.56637.

A = πr²/2; d = 2r; P = πr+2r

Worked example

Enter these known values and leave the other values blank.

Radius (r)
4 cm
Diameter (d)
8 cm
Area (A)
25.1327 cm²
Full boundary perimeter
20.5664 cm

Assumptions and limitations

  • The half disk spans 180 degrees. Full perimeter is the curved semicircular arc plus the straight diameter. Radius, diameter, area and perimeter are positive editable measures and use positive inverse roots. The captured hidden helper radius2 equals r²/2, has squared-length units and stays hidden; it is not a second public radius.
  • Clear unknown measurements before solving backward. Use compatible units and independent values. Reference pictures are original schematic drawings. Independently rounded measurements can fail strict compatibility at a boundary.
  • Where available, the soccer-field area option is a fixed 7,140 m² comparison (105 m by 68 m). Actual playing fields vary; it is not a survey or building unit.

Common questions

Does the perimeter include the diameter?

Yes. The full half-disk boundary is πr+2r. The curved semicircle by itself is only πr.

How do I use this calculator with different units?

Select the unit beside each measure. Length, squared length and volume use different dimensions; changing a unit preserves the physical value. Compound length controls represent feet/inches or meters/centimeters together.

References

The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

Explore circle calculators ⭕ or browse all math calculators.