Shaft Torque Calculator
Calculate Smarter. Work Faster.
Get shaft torque from power and rpm — then check what that torque does to the shaft: shear stress, angle of twist, torsional stiffness, shear strain and maximum torque capacity, for solid or hollow shafts.
Shaft Torque Inputs
Pick what you want to calculate, enter the drive data or shaft geometry, and get the answer instantly.
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Choose a mode and enter values to see how the result was reached.
Enter values above to see a step-by-step breakdown.
How Shaft Torque Is Calculated from Power and Speed
A rotating shaft carries power as a combination of torque (twisting effort) and speed. The same power can arrive as a lot of torque turning slowly, or a little torque turning fast — which is exactly the trade a gearbox makes. The relationship is:
Rearranged for torque, with power in watts and speed in rev/min:
The familiar 9550 simply packs those unit conversions into one number: 1000 × 60 ÷ 2π = 9549.3, rounded for everyday use. In imperial units the same relation reads T (lbf·ft) = 5252 × hp ÷ rpm, where 5252 is 33,000 ÷ 2π.
Worked example: a 15 kW motor at 1440 rpm gives T = 9550 × 15 ÷ 1440 = 99.5 N·m (10.1 kgf·m, 73.4 lbf·ft).
Which power figure to use. On an induction motor nameplate the kW rating is already rated mechanical output at the shaft, so it goes straight into the formula. If your figure is electrical input, or the shaft you care about sits behind a belt drive or gearbox, apply the efficiency first — the calculator's efficiency field does this for you.
Torque after a reduction. Speed falls by the ratio and torque rises by the same ratio, less losses. 10 N·m through a 20:1 reducer at 95% efficiency leaves about 190 N·m on the slow shaft. Always size each shaft for the torque it actually sees at its own speed.
Knowing the torque is only half the job, though. The next question is what that torque does inside the shaft — the stress it sets up, how much the shaft twists, and how close it is to its limit. That is what the remaining modes of this calculator cover.
Shear Stress and Polar Moment of Inertia
Torque in a circular shaft produces pure shear. The governing relation is the torsion equation:
where T is torque, J the polar moment of inertia, τ the shear stress at radius r, G the modulus of rigidity, θ the angle of twist and L the twisted length. Rearranged the two ways you normally need:
The second form is how you go from a known or allowable shear stress back to the torque the shaft is carrying — the mode labelled Torque from shear stress above.
Polar moment of inertia. J describes how the cross-section resists twisting:
Substituting J and r = d/2 into (4) gives the compact solid-shaft form:
Why the fourth power matters. Because J goes as d⁴, a 10% increase in diameter makes the shaft roughly 46% stiffer in torsion and about 33% stronger. It is nearly always cheaper to step up one stock size than to change material.
Why hollow shafts work. Shear stress is zero at the axis and maximum at the surface, so the metal in the middle earns very little. Boring a hole of half the outside diameter removes a quarter of the cross-sectional area but only about 6% of the torque capacity — which is why weight-critical drive shafts, from aerospace to motorsport, are hollow.
Angle of Twist and Torsional Stiffness
The same torsion equation, taken from its right-hand pair, gives how far one end of the shaft rotates relative to the other:
Torsional stiffness is simply the torque needed per unit of twist:
usually quoted in N·m per radian or N·m per degree. Stiffness is what decides how much a drivetrain winds up under load — it matters for positioning accuracy on machine tools and indexing drives, for torsional resonance in reciprocating machinery, and for how badly shock loads are amplified.
Typical limits. Precision and long line shafts are often held to a twist of the order of 0.25° per metre, but the real limit belongs to the application: a camshaft that shifts valve timing, a lead shaft that loses index accuracy, and a general-purpose drive shaft all tolerate very different amounts. Where twist governs rather than stress, the shaft has to be sized on stiffness — see the Shaft Diameter Calculator, which sizes on that basis directly.
Note that stress and stiffness scale differently with diameter: stress goes as d³ but twist as d⁴. A shaft can be comfortably within its stress limit and still twist far too much, particularly when it is long and slender. Always check both.
Shear Strain in a Twisted Shaft
Shear strain γ is the angular distortion the torque produces. It follows from Hooke's law in shear, and can equally be read off the geometry of the twist:
It is dimensionless and usually very small, so it is commonly quoted in microstrain (strain × 10⁶). A steel shaft at 40 MPa shear stress has γ = 40 / 79,300 ≈ 0.000504, or about 504 µε.
Like stress, strain is largest at the outer surface and falls linearly to zero at the axis, which is why torsional fatigue cracks start at the surface and why surface finish, keyway corners and fillet radii dominate real shaft life. It is also the quantity a shear-mode strain gauge rosette actually measures: bonding a rosette at 45° to the axis and reading the strain gives you torque on a running machine, using this same relation in reverse.
Maximum Torque a Shaft Can Transmit
Two separate limits apply, and the smaller one wins.
Allowable shear stress. ASME transmission-shaft practice, as commonly published in machine-design references, takes 56 MPa where no keyway allowance is needed and 42 MPa where a keyway is present. General shafting steels are commonly worked in the 40–60 MPa range. These are working stresses that already carry a design margin — they are not yield strengths, and feeding a yield value into the formula leaves essentially no safety factor.
What this calculation does not cover. Pure torsion is only part of the story for a real shaft. Anything carrying a gear, pulley or sprocket also bends, and combined bending and torsion normally calls for a larger diameter than torque alone — that is the job of the Shaft Diameter Calculator. Fatigue under fluctuating load, stress concentration at keyways and shoulders, and critical (whirling) speed on long shafts are further checks in their own right.
Torque Unit Conversions
| Unit | In newton metres | Where you meet it |
|---|---|---|
| 1 N·m | 1 | SI base unit for torque; motor and gearbox data |
| 1 kN·m | 1,000 | Large drives, mill and marine shafting |
| 1 kgf·m | 9.80665 | Older Indian and European nameplates, hand tools |
| 1 kgf·cm | 0.0980665 | Small motors, instruments |
| 1 lbf·ft | 1.35582 | US machinery ratings, bolt torque specs |
| 1 lbf·in | 0.112985 | Small fasteners, fractional-hp drives |
A handful of shortcuts worth remembering: T (N·m) = 9550 × kW ÷ rpm, T (lbf·ft) = 5252 × hp ÷ rpm, and 1 lbf·ft ≈ 1.356 N·m. Mixing systems halfway through is the most common source of order-of-magnitude errors, so convert everything before you start — or let the unit dropdowns above do it.
Shaft Torque at Common Power & Speed Combinations
| Power | 2880 rpm (2-pole) | 1440 rpm (4-pole) | 960 rpm (6-pole) | 720 rpm (8-pole) |
|---|---|---|---|---|
| 3.7 kW | 12.3 N·m | 24.5 N·m | 36.8 N·m | 49.1 N·m |
| 7.5 kW | 24.9 N·m | 49.7 N·m | 74.6 N·m | 99.5 N·m |
| 15 kW | 49.7 N·m | 99.5 N·m | 149.2 N·m | 199.0 N·m |
| 37 kW | 122.7 N·m | 245.4 N·m | 368.1 N·m | 490.8 N·m |
| 75 kW | 248.7 N·m | 497.4 N·m | 746.1 N·m | 994.8 N·m |
This is why a lower-speed motor of the same kW rating is always the bigger, heavier machine: at 720 rpm an 8-pole motor delivers four times the torque of a 2-pole one of identical power, and torque is what sets shaft, key, coupling and gearbox size. "Power" alone never describes a drive requirement — the same kW can mean wildly different mechanical duty depending on the speed it turns at.
Shaft Torque Calculation Examples
Example 1 — Torque from power and speed
A 15 kW motor at 1440 rpm: T = 9550 × 15 ÷ 1440 = 99.5 N·m — equal to 10.1 kgf·m or 73.4 lbf·ft. Through a 20:1 reducer at 95% efficiency, the output shaft sees about 1890 N·m at 72 rpm.
Example 2 — Stress and twist in a 40 mm solid shaft
Take that 99.5 N·m on a 40 mm steel shaft, 1 m long, G = 79.3 GPa. J = π × 40⁴ / 32 = 251,327 mm⁴; τ = T·r/J = 99,500 × 20 ÷ 251,327 ≈ 7.9 MPa; θ = T·L/(G·J) = 99,500 × 1000 ÷ (79,300 × 251,327) ≈ 0.00499 rad = 0.286° over the metre. Torsional stiffness k = G·J/L ≈ 19,930 N·m/rad, and shear strain γ = τ/G ≈ 100 µε. Comfortable on both counts.
Example 3 — Torque from a known shear stress (T = τ·J/r)
A shaft with J = 30 m⁴ and r = 4 m carrying a shear stress of 500 N/m²: T = 500 × 30 ÷ 4 = 3,750 N·m. The same form answers the practical version too — for a 50 mm solid shaft at an allowable 42 MPa, J = 613,592 mm⁴ and r = 25 mm, giving T = 42 × 613,592 ÷ 25 ≈ 1,031 N·m of capacity.
Example 4 — Hollow versus solid
Bore the 40 mm shaft out to a 20 mm hole: J drops from 251,327 to π(40⁴ − 20⁴)/32 = 235,619 mm⁴, a loss of just 6.25% in both capacity and stiffness — while 25% of the metal, and 25% of the rotating weight, is gone. That trade is the whole reason hollow drive shafts exist.
These results describe pure torsion in a plain circular shaft. They do not account for bending from overhung loads, axial thrust, fatigue under fluctuating torque, stress concentration at keyways, splines, shoulders and fillets, or critical (whirling) speed. For any safety-critical shaft, have the design checked by a qualified mechanical engineer against the applicable code before manufacture.
Common Mistakes When Calculating Shaft Torque
1. Using motor speed for a shaft behind a gearbox. Torque multiplies by the reduction ratio. Size every shaft for the torque at its own speed, not the motor's.
2. Mixing N·m and N·mm with MPa. With τ in N/mm² the torque must be in N·mm. Forgetting the ×1000 throws the stress out by a factor of a thousand.
3. Confusing torque with power. A high-kW machine at high speed can produce less torque than a small slow-speed one. Shaft, key and coupling sizes follow torque, never kW.
4. Using electrical input kW as shaft power. An induction motor nameplate kW is already shaft output. Taking an electrical input figure without applying efficiency overstates the torque.
5. Checking stress but not twist. A long slender shaft can pass the stress check comfortably and still wind up far more than the drive can tolerate. Stress goes as d³, twist as d⁴.
6. Treating yield strength as allowable shear stress. The allowable value already contains the design margin; the raw yield figure does not.
7. Applying solid-shaft formulas to a hollow shaft. Without the (dₒ⁴ − dᵢ⁴) term, J and therefore capacity are overstated.
8. Sizing on running torque alone. Direct-on-line starting, jams and reversals produce peaks well above nameplate torque — allow for them, or use a shock and fatigue factor approach.
9. Ignoring keyways and fillets. The calculated stress is for a plain shaft; a keyway removes metal and concentrates stress at exactly the point the drive is transmitted.
10. Forgetting derating on a VFD at low speed. A self-cooled motor turning slowly loses its own fan cooling, so continuous torque may need derating even though the drive can command it.
Frequently Asked Questions
Shaft torque, shear stress, twist and capacity — answered
What is the shaft torque formula? +
From a drive rating, T (N·m) = 60 × P (W) ÷ (2π × N), which simplifies to T = 9550 × P(kW) ÷ N(rpm). From the state of stress in the shaft itself, T = τ·J/r, where τ is the shear stress, J the polar moment of inertia and r the outer radius. Both describe the same torque — one from the power being transmitted, one from the stress that torque produces.
How do I calculate torque from horsepower and rpm? +
Convert horsepower to watts first (1 mechanical hp = 745.7 W), then use T = 60P ÷ (2πN). In imperial units the same relation is T (lbf·ft) = 5252 × hp ÷ rpm. A 20 hp drive at 1750 rpm gives about 60 lbf·ft, or 81.4 N·m.
Where does the constant 9550 come from? +
It packages the unit conversions in P = T × ω. With ω = 2πN/60 and power in kilowatts, T = 1000 × 60 × P ÷ (2πN) = 9549.3 × P(kW) ÷ N(rpm), rounded to 9550 in everyday use.
How do you calculate shear stress in a shaft from torque? +
Use τ = T·r/J. For a solid circular shaft J = πd⁴/32 and r = d/2, which reduces to τ = 16T/(πd³). Stress is highest at the outer surface and falls linearly to zero at the axis — which is why hollowing out the centre costs so little strength.
What is the polar moment of inertia of a shaft? +
It measures how the cross-section resists twisting. Solid circular shaft: J = πd⁴/32. Hollow shaft: J = π(dₒ⁴ − dᵢ⁴)/32. Because it depends on the fourth power of diameter, a 10% larger shaft is about 46% stiffer and 33% stronger in torsion.
What is the angle of twist formula for a shaft? +
θ = T·L/(G·J), with θ in radians, L the twisted length, G the modulus of rigidity (about 79.3 GPa for steel) and J the polar moment of inertia. Multiply by 180/π for degrees. Long or precision drives are often held to a twist of the order of 0.25° per metre, though the real limit depends on the application.
What is torsional stiffness and how is it calculated? +
Torsional stiffness is the torque needed per unit of twist, k = G·J/L, usually quoted in N·m per radian or per degree. It sets how much a drivetrain winds up, which matters for positioning accuracy, torsional resonance and how badly shock loads are amplified.
How do you find the shear strain in a twisted shaft? +
Shear strain at the surface is γ = τ/G, and geometrically γ = r·θ/L. It is dimensionless and usually tiny, so it is often quoted in microstrain (strain × 10⁶). For steel at 40 MPa shear stress, γ ≈ 0.0005, or about 500 µε.
What is the maximum torque a shaft can transmit? +
From strength, T_max = τ_allow·J/r, which for a solid shaft is π·τ_allow·d³/16. From stiffness, T_max = G·J·θ_permissible/L. The governing capacity is whichever is smaller, since the shaft has to satisfy both the stress limit and any twist limit.
Does a hollow shaft transmit less torque than a solid one? +
For the same outer diameter, yes — but by less than you might expect. A bore of half the outer diameter removes a quarter of the metal and only about 6% of the torque capacity, because the removed material sits near the axis where stress is lowest. For the same weight, a hollow shaft with a larger outer diameter beats a solid one.
What is the difference between torque and power? +
Torque is the twisting effort at the shaft, in N·m. Power is the rate of doing work — torque multiplied by angular velocity. The same power can appear as high torque at low speed or low torque at high speed, which is exactly what a gearbox trades between.
Should I use nameplate power or shaft output power? +
The kW figure on an induction motor nameplate is rated mechanical output at the shaft, so it can be used directly. If your figure is an electrical input rating, or the torque you need is downstream of a gearbox or belt drive, apply the relevant efficiency first using the efficiency field in this calculator.
How does torque change after a gearbox? +
Speed drops by the reduction ratio and torque rises by the same ratio, less the gearbox efficiency. 10 N·m through a 20:1 reducer at 95% efficiency gives about 190 N·m at the output shaft, turning at one twentieth of the input speed.
Does an induction motor hold full torque at reduced speed on a VFD? +
Below base frequency a VFD holds roughly constant torque capability, so power falls in proportion to speed. Above base frequency it moves into constant-power, field-weakening operation and available torque drops off. Self-cooled motors also lose fan cooling at low speed, so continuous torque may have to be derated.
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