Mechanical Engineering Calculator
Five everyday mechanical calculations in one place: gear ratio, output speed and torque with gear sizes from the module; power, torque and rpm from any two of them; bolt tightening torque for metric and UNC bolts by grade and lubrication; belt and pulley speed, belt length and wrap angle; and hydraulic cylinder push and pull force and speed. Each result shows its formula, in metric or US units.
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How to use it
- Choose the calculation: gears, torque and power, bolts, belts or a hydraulic cylinder.
- Pick metric or US units.
- Fill in the values you know; optional fields add extra results.
- Read the result, the details and the formula, and copy them if needed.
Why use this tool
Gear trains
Ratio, output speed and torque with efficiency, plus pitch and outside diameters and center distance from the module.
Horsepower and torque
Enter any two of power, torque and rpm to get the third, in hp and lb·ft or kW and N·m.
Bolt torque
M5 to M36 and 1/4 to 1 inch UNC, grades 8.8 to 12.9, SAE 5 and 8 and stainless, with real nut factors.
Belts and pulleys
Driven speed, belt speed, open belt length and wrap angle with a slip warning.
Hydraulic cylinders
Push and pull force from bore, rod and pressure, and speed from pump flow.
Formula shown
Every answer comes with the formula used, so you can check it or put it in a report.
Gear ratio, speed and torque
The gear ratio is the number of teeth on the driven gear divided by the teeth on the driving gear. A 20-tooth pinion driving a 60-tooth gear gives 3:1: the output turns at a third of the speed with three times the torque, less a little for friction. Gear trains multiply: two 3:1 stages make 9:1.
For metric gears the module sets the size: the pitch diameter is module × teeth, and two gears mesh at a center distance of module × (z₁ + z₂) ÷ 2. A module 2 gear with 20 teeth is 40 mm across at the pitch circle and 44 mm outside.
Horsepower from torque and rpm
Horsepower = torque (lb·ft) × rpm ÷ 5,252. That is why torque and horsepower curves cross at 5,252 rpm on every dyno chart. In metric, kW = N·m × rpm ÷ 9,549. An engine making 300 lb·ft at 4,000 rpm delivers 228 hp at that point.
Bolt torque chart (dry, 75% of proof load)
Torque is only a way to reach the right clamping force. About 90% of it is lost to friction under the head and in the threads, so lubrication changes the result a lot: oiled threads reach the same preload with roughly 25% less torque. Over-torquing a lubricated bolt with a dry value can stretch or break it.
| Bolt | Grade 5 / 8.8 | Grade 8 / 10.9 |
|---|---|---|
| 1/4-20 UNC | 8 lb·ft | 12 lb·ft |
| 3/8-16 UNC | 31 lb·ft | 44 lb·ft |
| 1/2-13 UNC | 75 lb·ft | 106 lb·ft |
| M8 (8.8 / 10.9) | 25 N·m | 36 N·m |
| M10 | 50 N·m | 72 N·m |
| M12 | 88 N·m | 126 N·m |
Hydraulic cylinder force
Force = pressure × piston area. A 3-inch bore at 2,000 psi pushes with 14,137 lbf, about 7 tons. On the return stroke the rod takes up part of the area, so pulling force and speed differ: a 1.5-inch rod leaves three quarters of the area, so the cylinder pulls with three quarters of the force and retracts a third faster.
Frequently asked questions
How do I calculate gear ratio?
Divide the driven gear's tooth count by the driving gear's. 60 ÷ 20 = 3, written 3:1. Output speed is input speed divided by the ratio; output torque is input torque times the ratio.
How do I convert torque to horsepower?
hp = lb·ft × rpm ÷ 5,252. In metric, kW = N·m × rpm ÷ 9,549.
How much torque for an M10 8.8 bolt?
About 50 N·m dry, or about 38 N·m oiled, for a preload of 75% of proof load. Use the manufacturer's value when there is one.
What is the nut factor K?
An empirical number that combines thread and head friction. 0.20 is typical for dry steel, 0.15 for oiled threads and 0.10 to 0.12 for anti-seize or moly paste.
How long a belt do I need?
L = 2C + π(D + d)/2 + (D − d)² / 4C, with C the center distance and D and d the pulley diameters. Choose the nearest standard length and adjust the center distance.
How much force does a hydraulic cylinder make?
Pressure times piston area. In metric, a 80 mm bore at 160 bar pushes about 80 kN, roughly 8 tonnes.
Everyday mechanical engineering calculations
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