Ratio-response curve with rating thresholdLive current inputs
Unit Converters
Torque Scale Calculator
Scale drivetrain torque without violating power conservation. The calculator separates ratio multiplication, efficiency loss, service-factor design demand, rated torque utilization, duty-adjusted thermal power, and the speed delivered to the driven machine.
Input evidence: use shaft torque at the declared duty point, actual speed ratio, manufacturer mesh efficiency, application-class service factor, continuous rating, and thermal rating from the same operating condition.
Delivered output torque-
Design torque-
Output speed-
Output power-
Rating utilization-
Limiting check-
Drivetrain scaling map
Separate kinematic multiplication, efficiency loss, and design allowance
The response curve shows output torque across ratio while the exact ledger reconciles power and ratings.
| Stage | Torque | Speed | Power | Adjustment | Decision use |
|---|
How to use
Check speed, delivered torque, design allowance, and heat as separate constraints
- Enter input torque and speed from the same operating point on the driver curve.
- Use the actual driven-to-driver speed ratio and a transmission efficiency measured or specified for the expected load.
- Select a service factor from the machine duty, shock, starts, reversals, and consequence of failure—not from a generic preference.
- Compare design torque with rated output torque and output power with the thermal limit.
- Review the response curve across plausible ratios before selecting a gearbox, belt drive, or chain stage.
Drivetrain fundamentals
A ratio redistributes speed and torque; it does not create power
The model separates kinematics, efficiency loss, application allowance, rating, and thermal duty so one favorable result cannot hide another governing constraint.
Matched-point rule: torque, speed, efficiency, rating, and thermal data must describe compatible operating conditions.
Calculation method
Conserve rotational power through the ratio and apply losses once
Output speed falls as ratio rises. Ideal torque rises by the same ratio, then transmission efficiency reduces delivered torque. The service factor converts delivered torque into a selection demand rather than another prediction of running torque.
nₒ = nᵢ ÷ i; Tₒ = Tᵢ × i × η; Tᵈ = Tₒ × SOutput speed follows the ratio, delivered output torque includes efficiency, and design torque includes the declared service factor.
- Do not multiply by efficiency twice when reconciling torque and power.
- Use rated torque at the calculated output speed, not a catalog maximum from another speed.
- Service factor is not a substitute for transient torque analysis.
- Thermal power can govern even when the mechanical torque rating passes.
Ratio selection
A larger ratio trades speed for torque
Increasing ratio shifts the operating point along a response curve. It can improve torque margin while making output speed unusable or moving the driver away from its efficient region.
- Confirm minimum and maximum usable output speed.
- Check driver torque at the corresponding input speed.
- Include ratio tolerance and slip where applicable.
- Evaluate multi-stage efficiency rather than assuming one constant value.
Duty and shock
Average load does not describe starts, jams, or reversals
Service factor should represent the real load spectrum and reliability consequence. Frequent starts, reversing duty, cyclic shock, and stalled conditions may require a time-domain or fatigue assessment.
- Record starts per hour and acceleration time.
- Separate running torque from breakaway torque.
- Check backdriving and braking loads.
- Use supplier duty classifications when they are available.
Decision interpretation
Mechanical pass, thermal pass, and usable speed must agree
Delivered torque estimates operating output; design torque is the selection demand. Rating utilization above 100% is a mechanical failure under the entered assumptions, while output power above the thermal limit indicates a heat-rejection problem even if torque passes.
How to read the ratio-response visual
The horizontal axis is ratio and the curve shows delivered or design torque as ratio changes; the rating line marks the entered torque capacity. Editing ratio moves the current operating point, while efficiency and service factor change its height. The visual can mislead if driver torque or efficiency varies materially across speed.
Thermal and supplier boundary
Catalog torque alone is not a complete selection
Confirm lubrication method, ambient temperature, mounting orientation, altitude, duty cycle, housing cooling, bearing loads, and permissible starts. A catalog thermal limit may assume continuous operation and specific oil temperature, while intermittent duty may require the supplier's thermal-cycle method.
- Use the same duty classification for mechanical and thermal ratings.
- Check shaft, key, coupling, and overhung-load limits separately.
- Confirm whether the listed efficiency is nominal, peak, or load dependent.
- Escalate to a transient model when acceleration energy or braking dominates.
Detailed calculation process
Reconcile speed, torque, and power
1. Output speed: nₒ = nᵢ ÷ i.
2. Delivered torque: Tₒ = Tᵢ × i × η.
3. Input power: Pᵢ = 2πnᵢTᵢ ÷ 60,000.
4. Output power: Pₒ = Pᵢ × η.
5. Design torque: Tᵈ = Tₒ × S; utilization = Tᵈ ÷ Tᵣ.
- nᵢ, nₒ
- input and output rotational speed; rpm
- i
- driven-to-driver ratio; dimensionless
- Tᵢ, Tₒ
- input and delivered output torque; N·m
- η
- transmission efficiency; decimal
- S
- application service factor; dimensionless
- Tᵣ
- rated output torque; N·m
- Pᵢ, Pₒ
- input and output mechanical power; kW
Default substitution and reconciliation
nₒ = 1,450 ÷ 3.2 = 453.125 rpm. Tₒ = 180 × 3.2 × 0.91 = 524.16 N·m, and Tᵈ = 524.16 × 1.35 = 707.616 N·m. Input power is 27.332 kW and output power is 24.872 kW. Recomputing power from 2π × 453.125 × 524.16 ÷ 60,000 returns 24.872 kW.
Evidence requirements
Use one matched rating set
- Driver torque-speed point and operating tolerance
- Ratio definition, stage count, and ratio tolerance
- Efficiency at load, speed, lubrication, and temperature
- Supplier mechanical and thermal rating revisions
- Duty cycle, starts, shock events, and ambient conditions
Scope and limitations
What this steady-state model excludes
- Acceleration inertia, torsional vibration, resonance, and backlash
- Time-varying efficiency, lubrication starvation, and wear
- Shaft bending, bearing life, keys, couplings, and overhung loads
- Regenerative braking, stall, jam release, and transient temperature rise
Key terminology
Drivetrain glossary
- Ratio
- Input speed divided by output speed under this calculator's convention.
- Efficiency
- Output mechanical power divided by input mechanical power.
- Service factor
- Selection allowance applied to delivered torque.
- Duty cycle
- Operating time divided by total cycle time.
- Thermal rating
- Power-loss boundary under stated cooling conditions.
- Breakaway torque
- Torque required to initiate motion from rest.
Practical examples
Two drivetrain decisions
Conveyor reduction
An engineer checks whether a larger ratio supplies starting torque without reducing belt speed below the production requirement; the mechanical rating passes but the service-factor demand governs.
Intermittent mixer
A mixer operates only 70% of the time but experiences high-viscosity starts. The team keeps the shock allowance and asks the supplier to verify thermal cycling rather than relying on average power alone.
Important note
Before relying on this result
The steady-state model excludes torsional dynamics, acceleration, tooth stress, bearings, fatigue, lubrication, misalignment, and vendor derating.
Additional Torque Scale Calculator questions
Does ratio create power?
No. It trades speed for torque while losses reduce output power.
Is service factor delivered torque?
No. It is a selection allowance.
Which ratio convention is used?
Driven speed reduction ratio, equal to driven divided by driver.
Why check thermal power?
A mechanically strong reducer may overheat under continuous duty.