How this instrument works
This instrument reports both sides of a gearbox's power balance at once: how fast the output shaft turns and how hard it twists, given what goes in on the input side. The two answers are linked, not independent — n_out = n_in ⁄ ratio sets the speed, and T_out = T_in × ratio × η sets the torque, and both trace back to the same physical fact, that a gear mesh trades one quantity for the other rather than creating power from nothing. Slow a shaft down by a factor of four and, minus a small loss, its torque climbs by close to that same factor.
Efficiency, η, is what keeps the torque equation honest. Every real mesh sheds a slice of the power passing through it to friction between tooth flanks, to bearing drag, and to the oil being churned inside the case, and that slice leaves as heat rather than torque at the output shaft. The number belongs on a gearbox's datasheet or nameplate; typical single-stage figures run 96–99% for a helical or spur mesh, 94–97% for a planetary stage, and as low as 50–90% for a worm gear, whose teeth slide rather than roll across each other. A mechanical engineer sizing a gearmotor for a mixer or conveyor reads this number off the reducer's spec sheet before trusting any torque figure downstream of it.
One limit worth knowing: this is a steady-state, continuous figure, not a strength rating. A gearbox's nameplate torque usually carries its own service factor on top, added to absorb starting surges, shock loads, and duty-cycle spikes that a plain speed-and-torque calculation does not see. Treat the torque this instrument returns as the running load flowing through the gears at the given speed, not as the maximum the housing, shafts, and bearings were built to survive.
- Enter Input speed, RPM — the rotational speed of the shaft feeding the gearbox.
- Enter Input torque — the twisting force delivered to that same shaft, in newton-metres.
- Set Gear ratio (input:output) — how many turns the input shaft makes per turn of the output shaft; use a value below 1 for an overdrive stage.
- Set Transmission efficiency as a decimal between 0 and 1, taken from the gearbox's datasheet or a typical figure for its gear type.
- Read Output speed, RPM and Output torque — the shaft speed and twisting force now leaving the gearbox.
Worked example — 4:1 reduction gearbox at 3,000 RPM
Consider a helical gear reducer feeding an industrial mixer: the motor shaft turns at 3,000 RPM and delivers 200 N·m into a 4:1 reduction, with the reducer's datasheet rating it 95% efficient. Output speed follows straight from the ratio, n_out = 3,000 ÷ 4 = 750 RPM — the mixer shaft turns once for every four turns of the motor.
Output torque needs the efficiency term folded in: T_out = 200 × 4 × 0.95 = 760 N·m. A lossless 4:1 stage would hand back exactly 800 N·m (200 × 4); the reducer's 5% loss — friction in the helical mesh and drag in its bearings — trims 40 N·m off that ideal figure, heat that the gearbox's housing has to shed rather than torque the mixer paddle receives.
Questions
Why isn't output torque simply input torque multiplied by the gear ratio?
Because a real gearbox is not perfectly efficient. The ideal, lossless torque gain is input torque times ratio, but the transmission efficiency term η — always below 1 — subtracts the share lost to friction between gear teeth, bearing drag, and oil churn inside the case. That lost share leaves as heat, not torque, which is why a 4:1 stage at 95% efficiency delivers 760 N·m rather than a full 800 N·m for 200 N·m in.
Can transmission efficiency be 1.0 or higher?
1.0 is the ceiling, not a target — it describes a hypothetical lossless gearbox and is useful only as a sanity-check upper bound. No real transmission reaches it, since some energy always leaves as friction heat, and a value above 1.0 would mean the gearbox creates energy, which violates conservation of energy. If a datasheet efficiency looks close to 1.0, expect 0.97–0.99 for a single well-cut helical stage, not a clean 1.0.
How do I estimate efficiency if the manufacturer doesn't list it?
Use a typical figure for the gear type doing the work. A single spur or helical stage usually runs 96–99% efficient, a planetary stage 94–97%, a bevel gear set in a right-angle drive 95–98%, and a worm gear anywhere from 50% to 90% depending on its lead angle and lubrication. When a real number exists on a nameplate or datasheet, use that instead — estimates are for early sizing, not final verification.
Which way does the gear ratio's input:output convention run?
A ratio of 4, entered as Gear ratio (input:output), means the input shaft turns four times for every single turn of the output shaft — a reduction. Enter a value below 1, such as 0.5, to describe an overdrive stage where the output spins faster than the input. Some manufacturers quote the reverse convention, output:input; if a datasheet's number looks inverted, take its reciprocal before entering it here.
How do I combine two or more gear stages in series?
Multiply the stages together separately for ratio and for efficiency, then enter the combined figures. Two 4:1 stages in series give an overall ratio of 16:1; two stages each 95% efficient combine to 0.95 × 0.95 = 90.25% overall, not 95%, since every stage sheds its own share of power. A long gear train can lose noticeably more than any single stage suggests.
Is the output torque here a continuous rating or a peak rating?
Continuous. The formula reports the steady torque flowing through the gearbox at the given speed and efficiency, not the momentary peak a gearbox can survive during a shock load or a stall. A manufacturer's nameplate rating usually applies a separate service factor on top of this figure to allow for starting surges and duty-cycle shocks, so treat this result as the running torque, not a strength limit.