Cycloid Calculator
Find the area, arc length, width, height and perimeter of one ordinary cycloid arch.
Formula
A = 3πr²; S = 8r; W = 2πr; H = 2r; P = S + W.
Rolling radius r: 2 cm · Area under arch ≈ 3×pi×(2 cm × 0.01 m/cm)^2×10000 · Arc length S ≈ 800×(2 cm × 0.01 m/cm) · Arch width W ≈ 200×pi×(2 cm × 0.01 m/cm) · Arch height H ≈ 200×(2 cm × 0.01 m/cm) · Closed perimeter P ≈ (16)+(12.56637061)
How to use
- Enter the rolling circle’s radius.
- Choose its length unit.
- Read results for one complete arch.
Examples
- Radius 2 cm: area ≈ 37.699112 cm²; arc length = 16 cm.
Frequently asked questions
What generates this curve?
A point on a circle rolling along a straight line without slipping.
What does perimeter include?
The curved arch plus the straight baseline between its two cusps.
Does this cover every cycloid variant?
No. These formulas describe the ordinary cycloid, not prolate, curtate, epi- or hypocycloids.
Sources
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