Perimeter of Cycloid Calculator

✖Radius of Circle of Cycloid is a radial line from the focus to any point of a curve of Cycloid.ⓘ Radius of Circle of Cycloid [r_Circle]

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✖The Perimeter of Cycloid is the total distance around the edge of the Cycloid.ⓘ Perimeter of Cycloid [P]

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Perimeter of Cycloid Solution

STEP 0: Pre-Calculation Summary

Formula Used

Perimeter of Cycloid = (8+(2*pi))*Radius of Circle of Cycloid
P = (8+(2*pi))*r_Circle
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Perimeter of Cycloid - (Measured in Meter) - The Perimeter of Cycloid is the total distance around the edge of the Cycloid.
Radius of Circle of Cycloid - (Measured in Meter) - Radius of Circle of Cycloid is a radial line from the focus to any point of a curve of Cycloid.

STEP 1: Convert Input(s) to Base Unit

Radius of Circle of Cycloid: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P = (8+(2*pi))*r_Circle --> (8+(2*pi))*5

Evaluating ... ...

P = 71.4159265358979

STEP 3: Convert Result to Output's Unit

71.4159265358979 Meter --> No Conversion Required

FINAL ANSWER

71.4159265358979 ≈ 71.41593 Meter <-- Perimeter of Cycloid

(Calculation completed in 00.004 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Indian Institute of Information Technology (IIIT), Bhopal

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< Perimeter of Cycloid Calculators

Perimeter of Cycloid given Base Length

LaTeX Go Perimeter of Cycloid = (8+(2*pi))*Base Length of Cycloid/(2*pi)

Perimeter of Cycloid

LaTeX Go Perimeter of Cycloid = (8+(2*pi))*Radius of Circle of Cycloid

Perimeter of Cycloid given Arc Length

LaTeX Go Perimeter of Cycloid = (8+(2*pi))*Arc Length of Cycloid/8

Perimeter of Cycloid given Height

LaTeX Go Perimeter of Cycloid = (8+(2*pi))*Height of Cycloid/2

Perimeter of Cycloid Formula

LaTeX Go

Perimeter of Cycloid = (8+(2*pi))*Radius of Circle of Cycloid
P = (8+(2*pi))*r_Circle

What is a Cycloid?

In geometry, a Cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve. The cycloid, with the cusps pointing upward, is the curve of fastest descent under constant gravity (the brachistochrone curve). It is also the form of a curve for which the period of an object in simple harmonic motion (rolling up and down repetitively) along the curve does not depend on the object's starting position (the tautochrone curve).

How to Calculate Perimeter of Cycloid?

Perimeter of Cycloid calculator uses Perimeter of Cycloid = (8+(2*pi))*Radius of Circle of Cycloid to calculate the Perimeter of Cycloid, The Perimeter of Cycloid formula is defined as the length of the outermost parts or boundary of a Cycloid. Perimeter of Cycloid is denoted by P symbol.

How to calculate Perimeter of Cycloid using this online calculator? To use this online calculator for Perimeter of Cycloid, enter Radius of Circle of Cycloid (r_Circle) and hit the calculate button. Here is how the Perimeter of Cycloid calculation can be explained with given input values -> 71.41593 = (8+(2*pi))*5.

FAQ

What is Perimeter of Cycloid?

The Perimeter of Cycloid formula is defined as the length of the outermost parts or boundary of a Cycloid and is represented as P = (8+(2*pi))*r_Circle or Perimeter of Cycloid = (8+(2*pi))*Radius of Circle of Cycloid. Radius of Circle of Cycloid is a radial line from the focus to any point of a curve of Cycloid.

How to calculate Perimeter of Cycloid?

The Perimeter of Cycloid formula is defined as the length of the outermost parts or boundary of a Cycloid is calculated using Perimeter of Cycloid = (8+(2*pi))*Radius of Circle of Cycloid. To calculate Perimeter of Cycloid, you need Radius of Circle of Cycloid (r_Circle). With our tool, you need to enter the respective value for Radius of Circle of Cycloid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Perimeter of Cycloid?

In this formula, Perimeter of Cycloid uses Radius of Circle of Cycloid. We can use 3 other way(s) to calculate the same, which is/are as follows -

Perimeter of Cycloid = (8+(2*pi))*Arc Length of Cycloid/8
Perimeter of Cycloid = (8+(2*pi))*Base Length of Cycloid/(2*pi)
Perimeter of Cycloid = (8+(2*pi))*Height of Cycloid/2

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