Arc Length of a Circle
Calculate the length of a circular arc from its central angle
Interactive Sandbox
Adjust values in real-time and observe mathematical cause-and-effect
Linear Scaling: Circumference scales directly in 1:1 proportion with radius.
Variable Mechanics
Roles, constraints & impacts
Radius
Radius (Distance from center to perimeter)
Central Angle
Formula Parameter
At a Glance
Gotchas, units & real-world use
Formula Nature & Mechanics
Linear Scaling: Circumference scales directly in 1:1 proportion with radius.
Common Mistakes & Traps
- Confusing radius (r) with diameter (d = 2r) — always halve the diameter if given.
- Forgetting to square the units (e.g. output is in m² or cm², not linear m).
- Using a rounded value of π too early in multi-step calculations.
Dimensional Analysis & Units
[Length] → Result in linear units (e.g., m, cm)
Real-World & Industry Application
Pipes & fluid dynamics, circular pizza sizing economics, circular foundation engineering, and satellite orbit perimeters.
Worked Example: Arc Length of a Circle
Given:
- r = 6
- theta = 90
- L = (90 / 360) × 2π(6)
- L = 0.25 × 37.70
- L = 9.42 units
Answer: 9.42
Frequently Asked Questions
What is the Arc Length of a Circle formula?
L = (θ / 360) × 2πr. Calculate the length of a circular arc from its central angle.
How do I calculate Arc Length of a Circle?
Enter Radius (r), Central Angle (theta) into the calculator. It applies L = (θ / 360) × 2πr and shows every step of the working.
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