Choose a pitch model and enter known values. See angle, trigonometric components, and unit checks. Download a report and reuse results in experiments today.
| Case | Inputs | Expected pitch angle |
|---|---|---|
| Helix geometry | Lead 5 mm, Mean diameter 20 mm | ≈ 4.55° |
| Velocity pitch | v∥ 12 m/s, v⊥ 5 m/s | ≈ 22.62° |
| Magnetic pitch | B∥ 0.30 T, B⊥ 0.12 T | ≈ 21.80° |
Use the same units within a model. The angle is dimensionless.
The pitch angle θ of a helix on a cylinder is defined by the ratio of axial advance to circumference:
tan(θ) = L / (π·D)
For helical motion with velocity components along and across a reference axis:
α = arctan(v⊥ / v∥)
For a helical magnetic field decomposed into parallel and perpendicular components:
α = arctan(B⊥ / B∥)
The pitch angle quantifies how strongly a trajectory, thread, or field line wraps around a reference axis. A small pitch angle indicates mostly axial behavior, while a larger pitch angle indicates stronger transverse winding. Because it is based on ratios, the pitch angle is dimensionless and can be reported in degrees or radians.
In geometry, a helix on a cylinder advances by a lead L over one revolution while the perimeter is \pi D. The calculator uses \tan(\theta)=L/(\pi D). In screws and conveyors, larger lead or smaller diameter increases θ and reduces axial mechanical advantage.
For helical motion, the pitch angle can be defined from velocity components: \alpha=\arctan(v_\perp/v_\parallel). In charged-particle motion, v_\perp relates to gyromotion and v_\parallel sets axial streaming. Using atan2 keeps the correct quadrant when v_\parallel is negative.
In magnetized systems, a similar definition applies to field components: \alpha=\arctan(B_\perp/B_\parallel). Increasing B_\perp at fixed B_\parallel increases α, meaning tighter twist around the guide field. This is useful for comparing helical field configurations.
The example helix case uses L=5 and D=20 (same length unit), giving \tan\theta=5/(\pi\cdot20)\approx0.0796 and \theta\approx4.55^{\circ}. For velocity inputs v_\parallel=12, v_\perp=5, the calculator gives \alpha\approx22.62^{\circ}. For magnetic inputs B_\parallel=0.30, B_\perp=0.12, it returns \alpha\approx21.80^{\circ}. The complementary angle (90°−θ) is often useful in component projections, and the provided sine and cosine values help verify geometry quickly.
When angles are small, \theta\approx L/(\pi D) is a useful approximation. Relative errors in L or D propagate directly into \tan\theta, so accurate diameter selection matters. Around 5^{\circ}, a 1% change in \tan\theta shifts θ by only a few hundredths of a degree.
For the helix model, any length unit works as long as L and D share it. The velocity and magnetic models similarly require consistent units within each component pair. After calculating, export the same input set to keep results reproducible.
Choose the model that matches your definition of pitch. For geometry, use the mean diameter where contact or tracing occurs. For vector components, define the axis and sign convention clearly. Comparing \sin, \cos, and \tan helps sanity-check the result.
Pitch is the axial spacing between adjacent threads. Lead is the axial advance per full revolution. For multi-start threads, lead equals pitch multiplied by the number of starts.
Pitch angle depends on the circumference where the helix is traced. Using the mean diameter approximates the effective path length between inner and outer thread surfaces, which is often the most representative geometry.
With the definitions used here, the pitch angle is returned by an arctangent and typically lies between −90° and +90°. Angles outside that range usually indicate a different reference axis or definition.
The calculator uses atan2 for component models, so the angle reflects the correct quadrant. A negative parallel component can shift the angle by 180° compared with a simple ratio-based arctangent.
Many applications treat perpendicular magnitudes as nonnegative by definition. If your system uses signed perpendicular components, enter the sign through the parallel component or interpret the angle with your chosen sign convention.
Plasma physics often defines particle pitch angle using velocity components relative to the magnetic field direction. Use the velocity model if you have v_\parallel and v_\perp; use the magnetic model for field-line geometry.
Exports include your selected model, the entered inputs with units, the computed angle in degrees and radians, helpful trigonometric values, and calculation notes. This supports consistent reporting and later verification.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.