03 // Bidirectional STEM Calculators // ENGINEERINGT_out = T_in × (N_out / N_in) × (η / 100)

Mechanical Gear Ratio & Output Torque Calculator

A mechanical gear reduction multiplies input pinion torque T_in by the tooth ratio (N_out / N_in) adjusted for mesh efficiency η, while dividing angular speed by the same gear ratio.

T_out = T_in × (N_out / N_in) × (η / 100)

Pick which value you want to calculate (or type into any field):Solving for: T_out — Output Driven Torque

Output Driven TorqueCalculated

Torque delivered at the output shaft in N·m

0.11,000,000.00

Input Pinion Torque

Motor or driver torque in N·m

0.1100,000.00

Driven Gear Teeth (or Diameter)

Tooth count on output gear

5500

unit

Driver Pinion Teeth

Tooth count on input pinion

5500

unit

Drivetrain Mesh Efficiency

Mechanical transmission efficiency in percent

20100

Calculated Result · Output Driven Torque (T_out)

190N·m

Converted units:

Step-by-Step Calculation

01Canonical Law: T_out = T_in × (N_out / N_in) × (η / 100)

02Given Inputs (Base Units): T_in = 50 N·m, N_out = 60, N_in = 15, η (%) = 95

03Solve for T_out (Output Driven Torque): T_out = 190 N·m

A mechanical gear reduction multiplies input pinion torque T_in by the tooth ratio (N_out / N_in) adjusted for mesh efficiency η, while dividing angular speed by the same gear ratio.

Real-World Reference Values

Single-Stage Helical / Spur Gearη = 97% – 99%

High efficiency involute tooth mesh

Planetary Gearbox Stageη = 94% – 97%

Compact high torque-density coaxial reduction

Worm Gear Reducerη = 50% – 85%

High single-stage reduction with self-locking capability

20-Row Comparison Table

Output Driven Torque (T_out) · Input Pinion Torque (T_in)

Compare across:

Mechanical Gear Ratio & Output Torque Calculator — Input Pinion Torque → Output Driven Torque
#	Input Pinion Torque (N·m)	Output Driven Torque (N·m)	Δ %
01	50 N·mCurrent	190 N·m	0.00%
02	726.4098 N·m	2,760.36 N·m	+1352.82%
03	1,452.72 N·m	5,520.33 N·m	+2805.44%
04	2,179.03 N·m	8,280.31 N·m	+4258.06%
05	2,905.34 N·m	11,040.29 N·m	+5710.68%
06	3,631.65 N·m	13,800.27 N·m	+7163.30%
07	4,357.96 N·m	16,560.24 N·m	+8615.92%
08	5,084.27 N·m	19,320.22 N·m	+10068.54%
09	5,810.58 N·m	22,080.20 N·m	+11521.16%
10	6,536.89 N·m	24,840.18 N·m	+12973.78%
11	7,263.20 N·m	27,600.15 N·m	+14426.40%
12	7,989.51 N·m	30,360.13 N·m	+15879.02%
13	8,715.82 N·m	33,120.11 N·m	+17331.64%
14	9,442.13 N·m	35,880.08 N·m	+18784.25%
15	10,168.44 N·m	38,640.06 N·m	+20236.87%
16	10,894.75 N·m	41,400.04 N·m	+21689.49%
17	11,621.06 N·m	44,160.02 N·m	+23142.11%
18	12,347.37 N·m	46,919.99 N·m	+24594.73%
19	13,073.68 N·m	49,679.97 N·m	+26047.35%
20	13,799.99 N·m	52,439.95 N·m	+27499.97%

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Frequently Asked Questions

How does the gear ratio N_out / N_in affect output RPM?+

Angular velocity scales inversely with tooth count: RPM_out = RPM_in × (N_in / N_out). A 4:1 torque multiplication reduces output speed to ¼.

Can I enter pulley pitch diameters instead of tooth counts?+

Yes. For timing belts, V-belts, and friction rollers, the ratio of pitch diameters (D_out / D_in) is identical to (N_out / N_in).

How do I switch torque units between N·m and lb·ft?+

Use the inline unit dropdown next to T_out or T_in to convert between Newton-meters (N·m) and Pound-feet (lb·ft).