Motor Gear Ratio & Output Calculator

Q: How do I calculate motor gear ratio?

ECParts defines gear ratio as G = input or motor shaft speed divided by output shaft speed. A 10:1 reduction therefore uses G = 10.

Q: How do I calculate output RPM from motor RPM?

Use nout = nin / G, where nin is motor or input RPM and G is the gear ratio under the ECParts input/output convention.

Q: How do I calculate required motor RPM from output RPM?

Use nin = nout × G. For a 300 RPM output and a 10:1 reduction, the motor must run at 3000 RPM.

Q: How do I calculate output torque after a gearbox?

Ideal output torque is τin × G. With gearbox efficiency, use τout = τin × G × ηg.

Q: How does gearbox efficiency affect output torque?

Efficiency reduces the ideal torque multiplication. A 10:1 gearbox with 90% efficiency has an effective torque multiplication of 9×.

Q: How do I calculate required motor torque?

Use τin = τout / (G × ηg). Efficiency must be greater than zero for a finite input torque result.

Q: How do I calculate the required gear ratio for a target speed?

Use Gspeed = motor RPM / target output RPM. This only satisfies the speed constraint.

Q: How do I calculate the required gear ratio for a target torque?

Use Gtorque = required output torque / (motor torque × gearbox efficiency).

Q: What does a 10:1 gear ratio mean?

With the adopted convention, 10:1 means the motor or input shaft turns about 10 revolutions for 1 output revolution.

Q: Does a gearbox increase motor power?

No. A gearbox trades speed for torque. Ideal mechanical power is conserved, and real output power is lower because of gearbox loss.

Calculate gearbox output RPM, output torque, required motor RPM, required motor torque, gear tooth ratio, multi-stage ratio, total gearbox efficiency, mechanical power balance, and gearbox loss for motor-drive sizing references.

MOT-009 uses one fixed convention: gear ratio G equals input or motor shaft speed divided by output shaft speed. A 10:1 reduction is therefore G = 10. Gearbox efficiency is mechanical gearbox efficiency, not motor electrical efficiency.

Engineering tool

Motor Gear Ratio & Output Calculator

Calculate motor gearbox output RPM, output torque, required input speed, required motor torque, gear tooth ratio, multi-stage ratio, efficiency, power balance and gearbox losses.

Calculation mode

Parameter panel

Motor / Input SpeedRPMTarget / Output SpeedRPMMotor / Input TorqueN·mRequired / Output TorqueN·mGear Ratio Ginput/outputGearbox Efficiency%Driver Gear Teethinteger teethDriven Gear Teethinteger teethStage Ratioscomma list, 2-6 stagesStage Efficienciescomma list, %Speed UnitTorque UnitEfficiency UnitPower Unit

Result console

Output RPM: 300RPM
Output Torque: 9N·m
Output Power: 282.743W
Gearbox Loss: 31.4159W

Motor speed and motor torque must describe the same operating point. Do not combine no-load RPM with stall torque as if they occur simultaneously.

Reference table

Motor gear ratio output reference values
Input Mechanical Power	314.159	W
Expected Pout = Pin × ηg	282.743	W
Power Balance Error	0	W
Torque Multiplication Factor	9	×

Motor Gear Ratio & Output Formula Audit

Motor gear ratio and output formula audit
Gear Ratio Definition	ECParts defines G = input/motor shaft speed divided by output shaft speed.
Reduction Convention	A 10:1 reduction uses G = 10, so nout = nin / G.
Overdrive Convention	Ratios below 1 are allowed and represent output speed greater than input speed.
Output Speed Formula	nout = nin / G.
Required Input Speed	nin = nout × G.
Ideal Output Torque	τout,ideal = τin × G.
Efficiency-Adjusted Torque	τout = τin × G × ηg.
Required Input Torque	τin = τout / (G × ηg).
Gearbox Efficiency	ηg is gearbox mechanical efficiency, not motor electrical efficiency.
Power Balance	Pout = τout × ωout and should equal Pin × ηg under the adopted model.
Double-Counting Protection	Efficiency is applied once through output torque; output power is then computed from τout × ωout.
Ratio from Speed	Gspeed = nin / nout.
Ratio from Torque	Gtorque = τout / (τin × ηg).
Gear Tooth Ratio	For a simple external pair, G = Zdriven / Zdriver.
Multi-Stage Ratio	Gtotal = G1 × G2 × ... × Gn.
Multi-Stage Efficiency	ηtotal = η1 × η2 × ... × ηn.
Motor Operating Point	Motor torque and motor speed must belong to the same operating point.
Stall / No-Load Boundary	Do not combine stall torque with no-load RPM as a real output point.
Backlash Boundary	Backlash, compliance and lost motion are not represented by ideal ratio equations.
Dynamic Torque Boundary	Acceleration torque and reflected inertia are outside V1.
MOT-001 Boundary	MOT-001 owns generic shaft torque, speed and power relationships.
MOT-005 Boundary	MOT-005 owns motor efficiency; this page only models gearbox mechanical efficiency.
MOT-008 Boundary	MOT-008 owns encoder RPM and encoder placement references.

Formula

Formula reference

Motor gear ratio and gearbox output formulas

Efficiency is applied once to output torque. Output mechanical power is then calculated from adjusted output torque and output speed.

G = nin / noutnout = nin / Gnin = nout × Gτout,ideal = τin × Gτout = τin × G × ηgτin = τout / (G × ηg)Pin = τin × ωinPout = τout × ωoutPout ≈ Pin × ηgPloss = Pin - PoutGteeth = Zdriven / ZdriverGtotal = G1 × G2 × ... × Gnηtotal = η1 × η2 × ... × ηn

Variable definitions

G: gear ratio using input speed divided by output speed
nin: motor or gearbox input speed
nout: gearbox output speed
τin: motor/input shaft torque
τout: gearbox output shaft torque
ηg: gearbox mechanical efficiency
Zdriver: driver gear teeth
Zdriven: driven gear teeth

Motor Gear Ratio & Output Formula Audit

Motor gear ratio and output formula audit
Gear Ratio Definition	G = input/motor shaft speed divided by output shaft speed.
Reduction Convention	10:1 reduction uses G = 10.
Overdrive Convention	G < 1 is allowed and represents output speed greater than input speed.
Output Speed Formula	nout = nin / G.
Required Input Speed Formula	nin = nout × G.
Ideal Output Torque Formula	τout,ideal = τin × G.
Efficiency-Adjusted Torque Formula	τout = τin × G × ηg.
Required Input Torque Formula	τin = τout / (G × ηg).
Gearbox Efficiency Definition	ηg is gearbox mechanical efficiency from 0 to 1, not motor electrical efficiency.
Power Balance	Pout = τout × ωout ≈ Pin × ηg.
Efficiency Double-Counting Protection	Efficiency is applied once in torque; output power is computed from adjusted torque and output speed.
Ratio from Speed	Gspeed = nin / nout.
Ratio from Torque	Gtorque = τout / (τin × ηg).
Gear Tooth Ratio	Simple external pair: G = Zdriven / Zdriver.
Multi-Stage Ratio	Gtotal = G1 × G2 × ... × Gn.
Multi-Stage Efficiency	ηtotal = η1 × η2 × ... × ηn.
Motor Operating-Point Boundary	Motor RPM and torque must be from the same operating point.
Stall Torque / No-Load Boundary	Stall torque and no-load RPM cannot be combined as a real gearmotor output point.
Backlash Boundary	Backlash, compliance and lost motion are outside the ideal ratio equations.
Dynamic Torque Boundary	Acceleration torque, inertia reflection and duty-cycle sizing are outside V1.
MOT-001 Scope Boundary	MOT-001 owns generic shaft power from torque and speed.
MOT-005 Scope Boundary	MOT-005 owns motor efficiency; MOT-009 owns gearbox mechanical efficiency.
MOT-008 Scope Boundary	MOT-008 owns encoder pulse/count RPM and encoder placement references.

Worked Examples

Motor gear ratio and output worked examples
Example	Calculation	Result
Output RPM	Motor = 3000 RPM, G = 10	Output = 300 RPM
Required Motor RPM	Output = 300 RPM, G = 10	Motor = 3000 RPM
Ideal Output Torque	τin = 1 N·m, G = 10, η = 100%	τout = 10 N·m
Efficiency Torque	τin = 1 N·m, G = 10, η = 90%	τout = 9 N·m
Required Input Torque	τout = 9 N·m, G = 10, η = 90%	τin = 1 N·m
Ratio from Speed	Motor = 3000 RPM, target = 300 RPM	G = 10
Ratio from Torque	τin = 1 N·m, target = 9 N·m, η = 0.9	G = 10
Gear Teeth Ratio	Driver = 20, driven = 100	G = 5
Gear Teeth Output	Input = 1000 RPM, 20 → 100 gear	Output = 200 RPM
Two Stages	G1 = 3, G2 = 4	Gtotal = 12
Two Efficiencies	η1 = 0.9, η2 = 0.8	ηtotal = 0.72
Multi-Stage Speed	Gtotal = 12, input = 1200 RPM	Output = 100 RPM
Multi-Stage Torque	τin = 1 N·m, Gtotal = 12, ηtotal = 0.72	τout = 8.64 N·m
Input Power	τ = 1 N·m, RPM = 3000	Pin ≈ 314.159 W
Output Power	G = 10, η = 0.9, output = 300 RPM and 9 N·m	Pout ≈ 282.743 W
Power Balance	Same example	Pout = 0.9 × Pin
Gearbox Loss	Same example	Loss ≈ 31.416 W
1:1 Ideal	G = 1, η = 1	Speed and torque unchanged
1:1 Lossy	G = 1, η = 0.8	Speed unchanged, torque = 0.8 × input
Overdrive Speed	G = 0.5, input = 1000 RPM	Output = 2000 RPM
Overdrive Torque	G = 0.5, η = 1, input = 10 N·m	Output = 5 N·m
Zero Efficiency	η = 0	Rejected
Over-Unity Efficiency	η = 120%	Rejected
Constraint Mismatch	Gspeed = 10, Gtorque = 12	Flag mismatch
Speed Round Trip	RPM → output → input	Original RPM recovered
Torque Round Trip	Torque → output → required input	Original torque recovered

Engineering Notes

Motor gear ratio and gearbox output engineering notes
Motor Gear Ratio	ECParts uses input speed divided by output speed for every MOT-009 mode.
Gear Reduction	A reduction lowers speed and raises torque under the adopted convention.
Gearbox	The model is an idealized mechanical transfer with a single efficiency term.
Output RPM	Output speed equals input speed divided by G.
Output Torque	Efficiency-adjusted output torque equals input torque times G times ηg.
Torque Multiplication	The effective torque multiplication factor is Gηg.
Gearbox Efficiency	Efficiency may vary with load, speed, lubrication, temperature and direction.
Mechanical Power	A gearbox does not create mechanical power; real output power is lower than input power.
Gear Teeth	A simple external driver/driven pair uses driven teeth divided by driver teeth.
Multi-Stage Gearbox	Stage ratios and stage efficiencies multiply.
Overdrive	G below 1 increases speed and reduces torque.
Backlash	Backlash and compliance affect motion but are not included in the ideal equations.
Motor Operating Point	Input torque and input speed must come from the same motor operating point.
Torque-Speed Curve	Changing the ratio changes the load line and can move the motor operating point.
Static Torque	V1 assumes steady shaft torque and does not include acceleration torque.
Non-Backdrivable Gearbox	Some worm or self-locking mechanisms cannot use one efficiency value for reverse drive.

Common Mistakes

Writing a 10:1 reduction as G = 0.1.
Multiplying output RPM by G instead of dividing input RPM by G.
Dividing output torque by G instead of multiplying input torque by G.
Applying gearbox efficiency twice.
Adding multi-stage efficiencies instead of multiplying them.
Adding multi-stage ratios instead of multiplying them.
Accepting efficiency above 100%.
Rejecting G < 1 instead of treating it as overdrive.
Swapping driver and driven gear teeth.
Combining stall torque with no-load RPM.
Confusing gearbox efficiency with motor electrical efficiency.
Treating remaining mechanical power as motor efficiency.
Ignoring that a new gear ratio can change the real motor operating point.
Assuming backlash-free positioning from ideal gear ratio alone.

Support reference

FAQ

How do I calculate motor gear ratio?

ECParts defines gear ratio as G = input or motor shaft speed divided by output shaft speed. A 10:1 reduction therefore uses G = 10.

How do I calculate output RPM from motor RPM?

Use nout = nin / G, where nin is motor or input RPM and G is the gear ratio under the ECParts input/output convention.

How do I calculate required motor RPM from output RPM?

Use nin = nout × G. For a 300 RPM output and a 10:1 reduction, the motor must run at 3000 RPM.

How do I calculate output torque after a gearbox?

Ideal output torque is τin × G. With gearbox efficiency, use τout = τin × G × ηg.

How does gearbox efficiency affect output torque?

Efficiency reduces the ideal torque multiplication. A 10:1 gearbox with 90% efficiency has an effective torque multiplication of 9×.

How do I calculate required motor torque?

Use τin = τout / (G × ηg). Efficiency must be greater than zero for a finite input torque result.

How do I calculate the required gear ratio for a target speed?

Use Gspeed = motor RPM / target output RPM. This only satisfies the speed constraint.

How do I calculate the required gear ratio for a target torque?

Use Gtorque = required output torque / (motor torque × gearbox efficiency).

What does a 10:1 gear ratio mean?

With the adopted convention, 10:1 means the motor or input shaft turns about 10 revolutions for 1 output revolution.

Does a gearbox increase motor power?

No. A gearbox trades speed for torque. Ideal mechanical power is conserved, and real output power is lower because of gearbox loss.

Why does torque increase when speed decreases?

For an ideal reduction gearbox, speed decreases by G while torque increases by G, keeping mechanical power approximately constant before losses.

How do I calculate gear ratio from gear teeth?

For a simple external gear pair, G = driven teeth / driver teeth. A 20-tooth driver and 100-tooth driven gear gives G = 5.

How do I calculate a multi-stage gear ratio?

Multiply the stage ratios: Gtotal = G1 × G2 × ... × Gn. Do not add the ratios.

How do I combine gearbox efficiencies?

Multiply the stage efficiencies as fractions. For 90% and 80%, ηtotal = 0.9 × 0.8 = 0.72.

What does a gear ratio below 1 mean?

Under the ECParts convention, G below 1 means overdrive or speed increase: output speed is greater than input speed and torque is reduced.

Does a gearbox change motor operating point?

Yes. Changing gear ratio can change motor load torque, speed, current and efficiency. This page is a kinematic and mechanical power reference, not a full motor selection model.

Can I combine motor stall torque with no-load RPM?

No. Stall torque and no-load speed occur at different operating points and must not be combined as one real output condition.

How does gearbox backlash affect output?

Motor Gear Ratio & Output Calculator

Parameter panel

Reference table

Motor Gear Ratio & Output Formula Audit

Formula

Motor gear ratio and gearbox output formulas

Variable definitions

Motor Gear Ratio & Output Formula Audit

Worked Examples

Engineering Notes

Common Mistakes

FAQ

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