Spline Calculator
This spline calculator estimates the torque a splined shaft connection can transmit, based on the bearing pressure the spline teeth can withstand. A spline is a set of teeth machined along a shaft that mesh with grooves in a hub, sharing the load across many contact faces so it carries far more torque than a single key. The capacity follows from the bearing on the tooth flanks: each tooth presents a contact area equal to its working depth times its length, the allowable pressure acts over that area, and the resulting force acts at the mean radius. Multiplying the allowable pressure by the number of teeth, the tooth depth, the length and the mean radius gives the transmissible torque, the standard simplified bearing-based estimate used in mechanical and automotive drivetrain design, including the work behind vehicle safety at the US National Highway Traffic Safety Administration. Enter the allowable bearing pressure, the number of splines, the tooth working depth, the engaged length and the mean radius, and the calculator returns the torque capacity in newton-millimeters and newton-meters. Every figure is computed deterministically from the bearing-torque formula shown in full below, with a worked example that reconciles exactly to the calculator so you can follow each step.
Torque capacity is the bearing pressure spread over every tooth at the mean radius: pressure 10 MPa on 6 splines of depth 4 mm, length 40 mm and mean radius 25 mm gives 240,000 N.mm, that is 240.00 N.m.
Spline torque capacity formula
T = p x N x h x L x r_m
p = allowable bearing pressure
N = number of splines, h = tooth working depth
L = engaged length, r_m = mean radius
Each tooth flank carries a bearing force equal to the allowable pressure times its contact area, the depth times the length. With N teeth all acting at the mean radius, the total torque is the pressure times the number of teeth times the depth times the length times the mean radius. This is the simplified, bearing-limited capacity.
Worked example
Find the torque capacity for 6 splines, allowable pressure 10 MPa, tooth depth 4 mm, length 40 mm and mean radius 25 mm.
- bearing area per tooth = h x L = 4 x 40 = 160 square mm
- force per tooth = p x area = 10 x 160 = 1,600 N
- total tangential force = N x 1,600 = 6 x 1,600 = 9,600 N
- T = force x mean radius = 9,600 x 25 = 240,000 N.mm = 240.00 N.m
The torque capacity is 240,000 N.mm, equal to 240.00 N.m. These are the calculator's default inputs, so the result above matches the widget exactly.
Capacity by number of splines
More teeth share the load, raising the bearing-limited torque proportionally.
| Splines | Torque (N.m) |
|---|---|
| 4 | 160.00 |
| 6 | 240.00 |
| 8 | 320.00 |
| 10 | 400.00 |
Drivetrain and transportation safety context: US National Highway Traffic Safety Administration (NHTSA).
Spline Calculator: frequently asked questions
Why does a spline carry more torque than a key?
A spline has many teeth that share the load, whereas a single key concentrates the whole tangential force on one small element. By spreading the bearing force across all the teeth, the spline keeps the pressure on each flank low while transmitting a much larger total torque, which is why splines are used in high-load drivetrains.
What is the mean radius?
The mean radius is the average of the spline's major and minor radii, the effective radius at which the tooth bearing force acts to produce torque. Using the mean radius reflects that the contact is distributed over the tooth height rather than concentrated at the outer edge.
What allowable pressure should I use?
The allowable bearing pressure depends on the material, the surface hardness and whether the connection is fixed or sliding under load. Published design guides give typical values, often in the range of several to a few tens of megapascals for steel splines. Enter the value appropriate to your application and duty.
Does every tooth share the load equally?
In an ideal spline all teeth share the load evenly, which is the assumption this simplified formula makes. In practice manufacturing tolerances mean some teeth carry more than others, so designers often apply a load-distribution factor that reduces the effective number of teeth. This tool gives the ideal bearing-limited capacity.
What units does the calculator use?
It uses SI units: bearing pressure in megapascals, lengths and radius in millimeters, and torque in newton-millimeters, which it also converts to newton-meters by dividing by 1,000. Keep all length inputs in millimeters so the areas and torque come out consistently.
Official sources
- Vehicle drivetrain and mechanical safety reference: US National Highway Traffic Safety Administration (NHTSA). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.