CALCULATE WITH CONFIDENCE

Engineering · Machine Design

Gear Tooth Force Components Calculator

Resolve an entered gear torque into ideal tangential, radial and—when selected—axial tooth-force components at the pitch diameter.

Engineering · Machine Design

Enter the engineering model

Explicit properties, geometry, units and assumptions
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example
Visual modelSchematic · not to scale
Machine Design: spurForce visual explanationA simplified diagram showing the relationship represented by the selected calculator mode. It is explanatory and not a fabrication, safety or scale drawing.tangential + radial spur-gear forcestorque becomes tangential force at pitch diameter
The diagram explains the selected relationship only. Dimensions, symbols and proportions are illustrative; use the entered values and stated assumptions for the calculation.

Keep every unit basis, sign convention, property source and idealization consistent. Values stay in this browser.

Engineering calculation result

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Enter valid values to see the result.

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Understand the machine model

What this calculator is for

Torque at a gear becomes tangential pitch-line force. Tooth geometry then introduces radial separation and, for helical gears, an axial component.

1Enter pitch diameter—not outside diameter.
2Select spur or helical geometry.
3Use rotation, mesh side and handedness to establish actual directions.

Visual explanation

Tangential force produces torque. The pressure angle tilts the contact force radially, while helix angle tilts part of it along the shaft.

The governing relationship

Ft=2T/d; spur Fr=Ft tanφ. Helical transverse relation uses Fr=Ft tanφt and Fa=Ft tanβ with entered transverse pressure angle φt.

Keep the boundary visible

Pitch-point force resolution only. Tooth sharing, dynamic factors, geometry factors, strength, contact stress, efficiency, bearings and standards remain outside scope.

Quick guide

How to use this calculator

  1. Choose the analysis mode that matches the physical model before entering values.
  2. Enter properties, geometry, loads, states and coefficients from one consistent unit and sign convention.
  3. Use the intermediate outputs to audit the relationship, then retain the stated idealization before applying it.

Calculation method

Transparent engineering model

Ft=2T/d; spur Fr=Ft tanφ. Helical transverse relation uses Fr=Ft tanφt and Fa=Ft tanβ with entered transverse pressure angle φt.

The calculator evaluates only the declared relationship and preserves visitor-entered assumptions rather than selecting materials, factors, components or standards.

Worked example

Worked example

A 500 N·m torque at a 0.2 m pitch diameter produces 5,000 N of ideal tangential tooth force.

Ft=2T/d; spur Fr=Ft tanφ. Helical transverse relation uses Fr=Ft tanφt and Fa=Ft tanβ with entered transverse pressure angle φt.

Supported inputs

Precision and limits

Analysis, not approval

Pitch-point force resolution only. Tooth sharing, dynamic factors, geometry factors, strength, contact stress, efficiency, bearings and standards remain outside scope.

Standards and properties

Material properties, allowable values, load combinations, safety factors, correlations, manufacturer data, codes and jurisdictional requirements are not supplied automatically.

Units and precision

Use one consistent unit basis. Results retain working precision but cannot be more accurate than the entered measurements and properties.

Privacy

Entered engineering values and results stay in this browser and are not sent to analytics or third parties.