How to use this calculator
- Choose load source. Use torque plus pitch diameter, or enter a known radial shaft load directly.
- Set drive factors. Enter the transmission factor and any load factor for shock or vibration.
- Enter bearing span. Use the distance between bearing reaction centers A and B.
- Place the load. Enter the load center position from bearing A; values outside 0 to L model an overhung load.
- Use the reactions. Use the bearing reactions for bearing sizing and the peak bending moment for shaft diameter or stress checks.
How it works
When torque is transmitted through a pulley, sprocket, pinion or gear, the first
radial-load estimate comes from the pitch radius:
F = (2T / D) x K x LF
where T is shaft torque, D is pitch diameter,
K is the transmission factor and LF is the load factor.
If the radial load is already known, the calculator uses that force directly
and applies only LF.
The shaft is then modeled as two bearing reaction centers: bearing A at
x = 0 and bearing B at x = L. Static equilibrium gives:
RB = F x / L and RA = F - RB. These signed reactions
work for both between-bearing and overhung loads. A negative reaction simply means
the bearing load acts in the opposite radial direction.
Peak bending moment is at the load point for a between-bearing load, at bearing A for a left overhang, and at bearing B for a right overhang. The calculator reports that moment in torque units so it can feed the shaft diameter calculator.
Worked example
Verified against the live calculator
A shaft transmits 200 N*m through a 120 mm pitch-diameter
pinion with transmission factor K = 1.25. The radial shaft load is
F = 2 x 200 / 0.12 x 1.25 = 4167 N.
If the bearings are 250 mm apart and the pinion load center is
320 mm from bearing A, the load overhangs 70 mm past
bearing B. The calculator gives RA = -1167 N,
RB = 5333 N, max bearing load 5333 N, load amplification
1.28, and peak bending moment 292 N*m at bearing B.
Frequently asked questions
How do you calculate overhung load from torque?
A common gearbox sizing estimate is overhung load F = 2T K / D, where T is shaft torque, D is pitch diameter of the pulley, sprocket, pinion or gear, and K is a connection factor for the drive type. This calculator also applies an optional load factor.
How do you calculate bearing reactions from an overhung load?
Model the shaft as two simple bearing supports separated by span L, with the radial load F at position x from bearing A. Static equilibrium gives RB = F x / L and RA = F - RB. If x is outside the span, one reaction becomes negative, meaning it acts in the opposite radial direction.
Why can a bearing reaction be larger than the applied load?
An overhung load creates a lever arm outside the bearing span. The nearest bearing may carry more than the applied radial load while the opposite bearing reacts in the opposite direction to balance moments.
Where is the peak bending moment?
If the load lies between the bearings, the peak moment is at the load point. If the load overhangs left of bearing A, the peak is at bearing A. If it overhangs right of bearing B, the peak is at bearing B.
Can this be used with gear mesh force?
Yes. Use the tangential/radial resultant or a single radial-plane component from the gear mesh, then enter its load center position along the shaft. Axial thrust is a separate bearing-catalog check.
Does this replace a bearing catalog calculation?
No. It finds radial reactions and bending moment for one load plane. Bearing selection still needs equivalent dynamic/static load factors, axial thrust handling, duty cycle, fit, lubrication, temperature and life rating.
Method & assumptions
- Single radial load in one plane acting on a shaft with two bearing reaction centers.
- Bearings are treated as simple supports; housing, bearing and shaft stiffness are not used for load sharing.
- For horizontal and vertical loads, calculate each plane and combine bearing loads by vector sum.
- Axial thrust, paired angular-contact/tapered-bearing preload and locating/floating bearing details are separate catalog checks.
- The overhung-load estimate uses pitch diameter. Use manufacturer-specific overhung-load limits when available.