Spiral Length Calculator
Calculate the length of Archimedean spirals and helical spirals around cylinders
Calculate Spiral Length
Total diameter of the spiral
Diameter of the center hole
Material thickness
Archimedean Spiral Results
Formula used: N = (D - d) / (2 × t), L = π × N × (D + d) / 2
Visual Representation
Spiral Formulas
Archimedean Spiral
Equation: r = a + b × θ
Turns: N = (D - d) / (2 × t)
Length: L = π × N × (D + d) / 2
Helical Spiral
Circumference: C = π × D
Length: L = √(H² + C²)
Based on: Pythagorean theorem
Common Applications
Archimedean Spirals
- • Paper rolls and tape rolls
- • Film reels and wire spools
- • Fabric and carpet rolls
- • Cable coils
Helical Spirals
- • Spiral staircases
- • Handrails and balustrades
- • Springs and coils
- • Helical strakes on towers
Example Calculations
Paper Roll
Outer diameter: 200 mm
Inner diameter: 40 mm
Paper thickness: 0.1 mm
Result: 1,256 m length
Spiral Staircase
Height: 3 m
Diameter: 2 m
Result: 7.21 m handrail length
Understanding Spiral Calculations
Archimedean Spiral
An Archimedean spiral is a curve where a point moves away from a fixed center at a constant rate while rotating. Named after the ancient Greek mathematician Archimedes, this spiral maintains equal spacing between successive turns.
Key Properties:
- •Constant separation distance between turns
- •Linear relationship between radius and angle
- •Used for calculating rolled material lengths
Helical Spiral
A helical spiral wraps around a cylinder in three dimensions, like a corkscrew or spiral staircase. The calculation uses the Pythagorean theorem to find the length of the spiral path.
Applications:
- •Architectural handrails and staircases
- •Industrial springs and coils
- •Helical strakes on chimneys and towers
Accuracy and Limitations
Archimedean Formula Accuracy
The simplified formula used here differs from the exact polar coordinate equation by less than 0.1%, making it highly practical for real-world applications where measurement precision is typically around 0.1%.
Helical Calculation
The helical formula assumes a single 360-degree turn around the cylinder. For multiple turns, multiply the result by the number of complete revolutions around the cylinder.