Free · Circle calculators ⭕

Quarter-Disk Arc Length and Full Boundary

No. The curved arc is πr/2. The full boundary adds two radii, so P = πr/2 + 2r.

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Calculator inputs

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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.

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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 Curved quarter arc L 6.283185, Full boundary perimeter 14.28319.

L = πr/2; P = L+2r

Worked example

Enter these known values and leave the other values blank.

Radius (r)
4 cm
Curved quarter arc L
6.28 cm
Full boundary perimeter
14.28 cm

Assumptions and limitations

  • The curved arc spans exactly 90 degrees. Full perimeter includes that arc plus both straight radii. Measures are positive. Radius alone calculates the other two; enter two compatible measures and clear the third to use its retained inverse. Perimeter alone does not populate radius in this captured equation workflow.
  • 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

Is the quarter arc the whole perimeter?

No. The curved arc is πr/2. The full boundary adds two radii, so P = πr/2 + 2r.

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 calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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