Helical Coil Calculator

Enter a coil's diameter, pitch, and number of turns to find its developed wire length, axial height, and pitch (helix) angle using standard helix geometry.

Quick Facts

Wire length per turn
ℓ = √((πD)² + p²)
Unrolling one turn of the helix gives a right triangle: one leg is the circumference πD, the other is the pitch p.
Pitch (helix) angle
α = arctan(p / (πD))
Also called the helix angle. Near 0° is a flat, tightly wound coil; larger angles advance faster per turn.
Coil axial length
H = N × p
The overall height (or length) the coil occupies along its central axis.

Your Results

Calculated
Total Wire Length
-
L = N × √((πD)² + p²)
Coil Axial Length (Height)
-
H = N × pitch
Pitch (Helix) Angle
-
α = arctan(pitch / (π × D))
Circumference per Turn
-
C = π × D

Ready

Enter the coil diameter, pitch, and number of turns, then press Calculate.

Formula and Method for the Helical Coil Calculator

A helical coil is formed by winding a wire, tube, or strip around a cylindrical axis while advancing steadily along that axis — the shape used in springs, wound inductors, cooling coils, and screw conveyors. This calculator finds the true (developed) length of material needed to form the coil, the coil's overall length along its axis, and the pitch (helix) angle, from three inputs: the coil's mean diameter, its pitch, and its number of turns.

How the calculation works

Unrolling one turn of a helix onto a flat surface turns the coiled path into the hypotenuse of a right triangle. One leg is the circumference the coil sweeps out each turn, C = πD, where D is the coil's mean (centerline) diameter; the other leg is the pitch p, the axial distance the coil advances during that same turn. By the Pythagorean theorem, the wire length used in one turn is ℓ = √(C² + p²) = √((πD)² + p²). Multiplying by the number of turns N gives the total developed wire length L = N × √((πD)² + p²). The coil's overall axial length (its height) is simply H = N × p, and the pitch (helix) angle — the angle between the wire and a plane perpendicular to the axis — is α = arctan(p / (πD)).

Common mistakes

  • Using the outer diameter instead of the mean diameter: measure to the centerline of the wire or tube, not its outside edge, or the calculated length and circumference will be slightly too large.
  • Confusing pitch with wire diameter: pitch is the axial distance between the centers of adjacent turns, not the thickness of the wire itself — a tightly wound coil can still have a pitch larger than the wire diameter if there are small gaps, or smaller if turns overlap is not allowed.
  • Forgetting what pitch = 0 means: a zero pitch collapses the coil into a flat spiral with zero axial height (H = N × p = 0), but the wire still travels the full circumference N times, so the wire length stays nonzero.

Real-world applications

  • Spring design: compression and extension springs are wound as helical coils, and the developed wire length determines how much raw wire stock is needed.
  • Heat-exchanger and cooling coils: tubing wound into a helix (immersion heaters, refrigeration coils, cooling coils) needs a known developed length to size pumps and estimate heat-transfer surface area.
  • Screw conveyors and augers: the pitch angle determines how steeply material advances along the axis with each revolution.
  • Wound inductors and helical antennas: the developed winding length feeds directly into resistance and wire-weight estimates.

Frequently Asked Questions

What is the formula for the length of wire in a helical coil?
Unroll one turn of the helix into a right triangle: one leg is the coil's circumference (C = πD, where D is the mean diameter), and the other leg is the pitch p (axial advance per turn). The wire length per turn is ℓ = √((πD)² + p²), and the total length for N turns is L = N × √((πD)² + p²).
How do I find the pitch angle of a helical coil?
The pitch (helix) angle is the angle between the coil's wire and a plane perpendicular to its axis: α = arctan(p / (πD)). A pitch angle near 0° describes a tightly wound, almost flat coil; a larger angle describes a coil that advances quickly along its axis with each turn.
Should I measure the outer diameter or the centerline diameter of the coil?
Use the mean (centerline) diameter — the diameter measured to the center of the wire or tube, not its outer edge. If you only have the outer diameter, subtract one wire diameter to estimate the mean diameter; using the outer diameter directly will slightly overstate the wire length and circumference.
What happens if I set the pitch to zero?
A pitch of zero produces a flat spiral with no axial height (H = N × p = 0), but the wire length calculation still returns a nonzero value equal to N times the circumference (πD), since the wire still travels around the coil N times.

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