Math / CALCULATOR

Point on a Standard Cycloid

Point on a Standard Cycloid with a worked example and explicitly bounded inputs.

Runs on your deviceUpdates as you typeFormula & example ↓
01

Your inputs

Adjust the values to explore a different result.

Enter rolling circle radius.
°
Enter rotation angle in °.

Formula

x=r(t−sin t); y=r(1−cos t); arc length from first cusp=4r(1−cos(t/2)).
  • Use the units shown beside each field.
  • Results update automatically whenever you change an input.
  • Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
  • One arch, circle rolling without slipping along a straight line. All lengths use the radius unit.

Example Calculation

Example inputs
  • Rolling circle radius: 1
  • Rotation angle: 180 °

Rolling circle radius = 1; Rotation angle = 180. Primary result: 3.141592653589793.

Frequently asked questions

How do I use this calculator?

Enter rolling circle radius, rotation angle. The result updates automatically. Use Reset to restore the example values.

What method does it use?

x=r(t−sin t); y=r(1−cos t); arc length from first cusp=4r(1−cos(t/2)).. One arch, circle rolling without slipping along a straight line. All lengths use the radius unit.

Why might a rounded result differ?

The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.

Are my inputs saved online?

No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.

Check the assumptions and units before using this result. Read about calculation methods.