Math

Spiral Length Calculator

Estimate the length of an Archimedean spiral.

Parameters Live Compute
Calculated Output
Approximate length 172.79
Formula: length ≈ π × turns × (inner + outer)
Step-by-Step Breakdown
1. Values used:
2. Inner radius = 1
3. Outer radius = 10
4. Number of turns = 5
5.
6. Approximate length = 172.79
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Estimate how long a spiral is — like a rolled tape, wire or clock spring.

The math behind it

Treating each loop as a circle whose radius grows steadily, the total length is about π × turns × (inner radius + outer radius).

Worked Example

Inner 1, outer 10, 5 turns → π·5·11 ≈ 172.8.

Frequently Asked Questions

How accurate is this?

It's a close approximation for evenly spaced spirals; exact length needs an integral.

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