Gear Torque Calculator

Once, I hear teeth click in my head. I see one gear push another. Why does a small gear make a big push at the other side? Because gears swap speed for torque. That swap is clean. That swap is math. We use a Gear Torque Calculator to make it easy.

Gear torque means the twist on a gear shaft. One gear gives torque to the next. Ratio sets how much it grows or shrinks. Power stays near the same, minus losses. If speed goes down, torque goes up.

If speed goes up, torque goes down. Simple, right? The calculator takes speed, power, ratio, and efficiency. It gives torque on input and output. It saves time. It saves mistakes.

How to calculate gear torque

I am an instructor on a small test rig. I stand with a learner. We run a motor and a gearbox. The motor gives 1.5 kW at 1500 rpm. We use a gear pair with 20 teeth on the pinion and 60 teeth on the gear. That is a 3:1 ratio. The gearbox efficiency is 92%. We ask: what is input torque? What is output speed and torque? We also check if the shaft can take it.

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Step-by-step calculation with formula

Step 1: Know basic formulas.

Power relation: P = T × ω
Angular speed: ω = 2π × RPM / 60
Gear ratio by teeth: i = Z2 / Z1
Output speed: n_out = n_in / i
Output torque with losses: T_out = T_in × i × η
Input torque from power: T_in = P / ω

Step 2: List given numbers.

P_in = 1.5 kW = 1500 W
n_in = 1500 rpm
Teeth: Z1 = 20 (pinion), Z2 = 60 (gear)
Ratio i = 60 / 20 = 3
Efficiency η = 0.92

Step 3: Convert input speed to rad/s.

ω_in = 2π × 1500 / 60
ω_in = 2π × 25 = 50π ≈ 157.08 rad/s

Step 4: Compute input torque.

T_in = P_in / ω_in = 1500 / 157.08 ≈ 9.55 N·m

Step 5: Compute output speed.

n_out = n_in / i = 1500 / 3 = 500 rpm

Step 6: Compute ideal output torque without losses (for feel).

T_out,ideal = T_in × i = 9.55 × 3 ≈ 28.65 N·m

Step 7: Apply efficiency to get real output torque.

T_out = T_in × i × η = 9.55 × 3 × 0.92
First 9.55 × 3 = 28.65
Then 28.65 × 0.92 ≈ 26.36 N·m

Step 8: Quick power check at output.

ω_out = 2π × 500 / 60 ≈ 52.36 rad/s
P_out = T_out × ω_out ≈ 26.36 × 52.36 ≈ 1,379 W
Loss ≈ 1500 − 1379 = 121 W, which fits η = 0.92.

Step 9: Tooth force at pitch radius (optional sanity).

If the gear pitch radius r2 = 0.06 m (assume), tangential force Ft ≈ T_out / r2
Ft ≈ 26.36 / 0.06 ≈ 439 N
Use this for tooth stress checks if needed.

Notes that help:

Higher ratio gives higher torque and lower speed.
Losses cut torque. Chain more stages and efficiency drops further.
For helical gears, add thrust loads, but torque math stays same.

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Why we care here:

The shaft, key, and gear must handle about 26 N·m.
The motor current spike on start may be higher. Plan safety margin.
If we need 40 N·m, we can raise ratio or raise motor power.

FAQs

Does gear torque change with time?

Under steady load, it stays steady. With shock or start, it spikes. Use service factors for real duty.

How do I get ratio from speed?

i = n_in / n_out. If you know speeds, you can find teeth ratio you need.

What if I only know horsepower?

Convert to watts. 1 hp ≈ 746 W. Then use T = P / ω to get input torque.

Final words and a short trick:

Manual trick: T_in ≈ 9550 × P(kW) / RPM. Then T_out ≈ T_in × i × η. Output speed = RPM_in / i. Keep η in decimal.
Why use the calculator: it handles units, ratios, multi-stage losses, and gives fast what-if runs. You get the right torque without slips.

Gear Torque Calculator