Spline Torque Capacity Calculator

Torque capacity of an involute or straight-sided spline against all three published limits — tooth shear, flank compressive stress and torsional shear of the shaft under the teeth — with the smallest governing, the fraction of teeth actually carrying as an input, Dudley’s load distribution factor, and the factor of nine between a fixed and a flexible spline.

Last updated 24 Sep 2026

Spline torque capacity

Spline geometry → three limits, smallest governs

Spline familyThe involute geometry is computable from the definition: pitch diameter is N/P for a diametral-pitch spline and m·N for a module one. Straight-sided splines are a table, so you enter the diameters.

Diametral pitch P (per inch), or module m (mm)For an ANSI B92.1 spline this is the FIRST number of the pitch pair: a 16/32 spline has P = 16 and its tooth height is set by the 32. Ignored for a straight-sided spline.

Number of teeth or splinesPitch diameter is N/P, so the tooth count and the pitch between them fix the size. More teeth at the same pitch means a bigger spline, not a stronger one at the same size.

Effective face width (mm)The length actually in contact, not the hub length. Beyond about one pitch diameter the far end carries little, for the same reason a long key does not: the shaft twists.

Straight-sided spline: major diameter D (mm)Only used for the straight-sided family.

Straight-sided spline: minor diameter d (mm)

Straight-sided spline: spline width B (mm)

Radial contact height h (mm, 0 to use the default)The radial height of flank actually in contact. The default for an involute spline is one addendum, 0.5/P, which this batch verified against six published ANSI B92.1 shaft diameters. Your drawing’s form diameters give the real figure and it is usually a little larger.

Bore through the shaft (mm, 0 for solid)A bore barely weakens the torsional section but it is the difference between the third limit mattering and not.

Torque to transmit (N·m)The torque the spline actually sees, including whatever service or shock factor your drive needs. This page does not apply one for you.

Load distribution factor K_mDudley’s misalignment factor. 1.0 for a short, well-aligned spline; 2 to 3 for a wide face with real misalignment. Two published readings of his table are printed below and they disagree.

Percentage of teeth actually carrying load (%)Dudley’s shear equation assumes 50%, because of spacing errors, and says to drop to about 33% with poor manufacturing accuracy. The flank-bearing equation assumes 100%, which becomes true after some initial wear.

Fixed or flexible splineA flexible spline is allowed to move under load, and it wears instead of yielding. Its allowable flank pressure is about a ninth of a fixed spline’s.

Allowable shear stress (N/mm²)Used for both the tooth shear and the shaft torsion. Published guidance is about 0.4 of the yield strength.

Allowable flank compressive stress, FIXED spline (N/mm²)Published guidance for a fixed spline is 0.45 to 0.6 of yield. Choosing “flexible” above divides this by nine, which is the ratio Dudley’s equations imply and a second publisher states in words.

Not a circuit: one spline tooth in section on its pitch line, with the three places a spline fails marked, and the three utilisations drawn as bars to ONE scale so the governing limit is a length rather than a number you have to compare. ① is the shear plane at the pitch line, hatched — the tooth shears off across its own thickness, and only the fraction of teeth you entered is assumed to be carrying when it happens. ② is the flank, where the compressive stress acts; that limit assumes every tooth is working, which Dudley says becomes true after some initial wear. ③ is the arc below, the shaft actually left under the teeth, whose torsional capacity does not improve at all when you make the spline longer. The tooth's radial height is drawn to scale against the pitch diameter, quantised to fortieths. The line across the bars is 100 per cent.

1,379N·mExample

A 24-tooth 16/32 involute spline, 38 mm of effective face, fixed, carrying 900 N·m with K_m = 1.5 and half the teeth assumed to bear

Three limits, the smallest of which is the answer

1. tooth shear S_s = 4T·K_m / (D·N·F_e·t_c), the 4 being 2 ÷ the fraction of teeth carrying · 2. flank bearing S_c = 2T·K_m / (D·N·F_e·h) · 3. shaft torsion S_s = 16T / (π·D_re³) · capacity = min of the three

D: pitch diameter. N/P for a diametral-pitch spline, m·N for a module one — an arithmetic consequence of what a pitch is, verified against six published catalogue shafts
N: number of teeth. Note that the shear equation multiplies by N and then divides by the fraction actually carrying, so a spline with more teeth is not proportionally stronger unless they all bear
F_e: effective face width — the length in contact. Limits 1 and 2 scale with it; limit 3 does not
t_c: circular tooth thickness at the pitch line. Half the circular pitch, π/(2P) or πm/2. One secondary source prints this as D/2N, which is short by a factor of π; the force balance behind Dudley’s equation settles it
h: radial height of flank in contact. Default is one addendum; your drawing’s form diameters give the real figure
K_m: Dudley’s load distribution factor for misalignment. 1 to 3, and two published readings of his table disagree in the middle
D_re: the diameter of the shaft actually left under the teeth. Pitch diameter less twice the contact height, which is the conservative reading

Worked example

A 24-tooth 16/32 involute spline, 38 mm of effective face, fixed, carrying 900 N·m with K_m = 1.5 and half the teeth assumed to bear
Geometry first, from the definition: pitch diameter = N/P = 24/16 = 1.5 in = 38.10 mm. Circular pitch is π/P and the tooth is half of it, so t_c = π/(2 × 16) = 2.494 mm. The addendum is 0.5/P = 0.794 mm, which is what six published ANSI B92.1 shafts confirm to five decimal places
Tangential force at the pitch circle: 2T/D = 2 × 900,000/38.10 = 47.24 kN
Limit 1, tooth shear. With half the 24 teeth carrying, the shear area is 12 × 38 × 2.494 = 1,137 mm², so the stress is 47.24 kN × 1.5 / 1,137 = 62.3 N/mm². At an allowable of 200 that is a capacity of 2,888 N·m
Limit 2, flank bearing. All 24 teeth, after wear-in: 24 × 38 × 0.794 = 724 mm² of flank, giving 97.9 N/mm² and a capacity of 1,379 N·m at 150 allowable
Limit 3, the shaft under the teeth. The section left is 38.10 − 2 × 0.794 = 36.51 mm, so W_t = π D³/16 = 9.558 kmm³ and the torsional shear is 94.2 N/mm² — a capacity of 1,912 N·m
The smallest wins: 1,379 N·m, on flank bearing. The 900 N·m asked for is 65% of that
Now change one thing. Drop the fraction of teeth carrying from 50% to 25% — which is the pessimistic end of published practice and what an inaccurately cut spline really does — and the shear stress DOUBLES to 124.6 N/mm² while the flank pressure does not move at all. That asymmetry is not an inconsistency in the method; it is Dudley's own statement that spacing errors decide which teeth shear while wear eventually spreads the flank load across all of them
And make the spline flexible instead of fixed: the allowable flank pressure divides by nine, to 16.7 N/mm², and the bearing capacity collapses to 153 N·m. A spline that is allowed to move is a wear problem, and wear does not care what the yield strength is

Why this page can compute the involute geometry instead of tabulating it

Six published ANSI B92.1 spline shafts from one manufacturer’s catalogue. Take the pitch diameter as N/P — which is what a diametral pitch MEANS, not a measurement — and the addendum that the published outside diameter implies comes out at exactly 0.5/P at every row, across two different pitches and four tooth counts. The last column is 1.000 six times. That is the check that the geometry on this page is the real geometry: nothing was fitted to these numbers and they were not used to derive anything, they were used to test a relation that comes from the definition. It is also where the default radial contact height comes from — one addendum, which is conservative, because a side-fit spline’s real flank contact band depends on the internal spline’s minor diameter too and that is on your drawing rather than in any catalogue. These dimensions come from a published standard’s table, not from a formula. The standard itself is cited below and the printed values are attributed to the catalogue they were taken from; a different publisher may round differently in the last digit.
Catalogue designation	Teeth N	Diametral pitch P	N/P (in)	Pitch diameter (mm)	Published outside Ø (in)	Addendum (in)	0.5/P (in)	Addendum ÷ (0.5/P)
30-16/32-9	9	16	0.5625	14.29	0.625	0.03125	0.03125	1.000
30-16/32-13	13	16	0.8125	20.64	0.875	0.03125	0.03125	1.000
30-16/32-15	15	16	0.9375	23.81	1.000	0.03125	0.03125	1.000
30-16/32-21	21	16	1.3125	33.34	1.375	0.03125	0.03125	1.000
30-12/24-14	14	12	1.1667	29.63	1.250	0.04167	0.04167	1.000
30-12/24-20	20	12	1.6667	42.33	1.750	0.04167	0.04167	1.000

Dudley’s five failure modes, and which of them this page checks

Three of the five are checked and two are named and refused. That distribution is itself the message: a spline has more ways to fail than a key does, the published closed-form methods cover some of them, and the ones they do not cover are not less dangerous for being harder to compute. A spline that strips is not a repairable condition. This page sizes a part; it does not certify one. Where the answer carries a consequence — a load path, a lifting duty, a pressure boundary, a fastener holding something that can fall — confirm it against the design code that governs the application, and against the manufacturer’s own rating, before relying on it.
Failure	Dudley’s description	Checked here?
Shaft breaks under the teeth	“Shaft of externally toothed member breaks underneath spline teeth”	YES — limit 3, the torsional shear on the section left under the spline. It is the one people forget, and it is the only one that does not improve when you make the spline longer
Teeth shear off	“Teeth of spline shear off on pitch line”	YES — limit 1, with the fraction of teeth actually carrying as an input rather than an assumption
Teeth break at the root	“Teeth break at roots in cantilever-type failure”	NO. A bending calculation on a spline tooth needs the tooth’s root geometry and a form factor, and this batch could not source either for the standard tooth forms. It is the mode that governs short, coarse-pitch splines under shock, and it is refused rather than guessed
Surfaces wear by fretting corrosion	“Contacting surface wears by fretting corrosion”	PARTLY. The flexible-spline flank pressure limit IS the wear criterion, divided by nine relative to a fixed spline. But no life in hours or cycles comes out of it, because the allowable pressures are calibrated to “acceptable wear”, not to a rate
The internally toothed member ruptures	“Shell of internally toothed member ruptures”	NO. That is a hoop-stress problem in the hub wall and it depends on the hub’s outside diameter, which this page does not ask for. A thin-walled internally splined hub is a real failure and the hoop stress belongs on the interference-fit page’s kind of calculation

The load distribution factor K_m: two published readings of the same table, printed side by side

The first four numeric columns are as Geepro Hobbing print Dudley’s Table IV; the last four are as the table came out of Dudley’s own 1957 paper in this batch’s reading of it. They agree at the extremes and disagree in the middle, and neither is averaged into the other, because the honest thing to do with two readings of one table is to show both. There is a third position and it is the one worth acting on: *Gear Solutions*‘ finite-element work finds that “Dudley’s table of misalignment factors is shown to under-predict the misalignment factor for some long L/D splines”, with the data splitting into a power law at L/D = 1.0 and a near-linear trend at L/D = 0.2. So K_m is an input on this page rather than a lookup. If you have no basis for it, 1.0 is only defensible for a short spline on a rigid, well-aligned assembly. The same designation can mean different dimensions in different standards families — ANSI against ISO, inch against metric, one national standard against another. The family used here is named beside every figure; check which one your part was made to.
Misalignment (in/in)	½ in face	1 in	2 in	4 in	½ in face	1 in	2 in	4 in
0.001	1.0	1.0	1.0	1.0	—	—	—	—
0.002	1.0	1.0	1.5	2.0	1.0	1.5	2.0	2.5
0.004	1.0	1.5	2.0	2.5	1.0	1.5	2.0	2.5
0.008	1.5	1.5	2.0	3.0	1.5	2.0	2.5	3.0

Dudley’s allowable flank pressures, and what fixed against flexible really costs

Two ratios in this table are worth more than the numbers. Crowning multiplies the allowable pressure by exactly four at every one of the five rows — not approximately, exactly — which tells you the column is a rule applied to one set of figures rather than five independent measurements. And a FIXED spline is allowed about nine times a flexible one: that follows from Dudley’s own Eq (6) and (7), where the flexible criterion carries an 8 and the fixed one a 9·K_a, and Geepro Hobbing state it in words — “fixed spline can carry 9 times more compressive stresses than flexible spline”. The reason is that a flexible spline is a WEAR problem, not a strength problem: it slides under load every revolution and the allowable pressure is set by how long the flanks last, which is why crowning — concentrating contact in the middle where it can roll rather than at the ends where it digs in — buys a factor of four. The same designation can mean different dimensions in different standards families — ANSI against ISO, inch against metric, one national standard against another. The family used here is named beside every figure; check which one your part was made to.
Material	Hardness	Flexible, straight teeth (psi)	(N/mm²)	Flexible, crowned teeth (psi)	(N/mm²)	Fixed spline, 9 × the straight figure (N/mm²)
Steel	160-200 HB	1,500	10.3	6,000	41.4	93
Steel	230-260 HB	2,000	13.8	8,000	55.2	124
Steel	302-351 HB (33-38 HRC)	3,000	20.7	12,000	82.7	186
Surface-hardened steel	48-53 HRC	4,000	27.6	16,000	110.3	248
Case-hardened steel	58-63 HRC	5,000	34.5	20,000	137.9	310

Straight-sided splines, ISO 14 / DIN 5463, light and medium series

The last column is why straight-sided splines lost. A straight-sided spline puts between about a quarter and a third of the circumference into teeth; an involute spline at standard proportions puts half of it into teeth, because its tooth thickness at the pitch line is half the circular pitch by definition. That is roughly twice the shear area in the same envelope, before any of the involute’s other advantages — it can be cut with a hob or shaped with the same tooling as a gear, it self-centres under load, and its root is a fillet rather than a corner. Straight-sided splines survive in older machine tools, in hydraulic pump drives and wherever a flat flank is wanted for a sliding fit. The mean radius and contact height here are geometry, not standard values: (D + d)/4 and (D − d)/2. These dimensions come from a published standard’s table, not from a formula. The standard itself is cited below and the printed values are attributed to the catalogue they were taken from; a different publisher may round differently in the last digit.
Series	N	d (mm)	D (mm)	B (mm)	Mean radius (mm)	Radial contact height (mm)	Tooth width as % of the circumference at the mean radius
light	6	23	26	6.0	12.25	1.50	46.8
light	6	26	30	6.0	14.00	2.00	40.9
light	6	28	32	7.0	15.00	2.00	44.6
light	8	32	36	6.0	17.00	2.00	44.9
light	8	36	40	7.0	19.00	2.00	46.9
light	8	42	46	8.0	22.00	2.00	46.3
light	8	46	50	9.0	24.00	2.00	47.7
light	8	52	58	10.0	27.50	3.00	46.3
light	8	56	62	10.0	29.50	3.00	43.2
light	8	62	68	12.0	32.50	3.00	47.0
medium	6	11	14	3.0	6.25	1.50	45.8
medium	6	13	16	3.5	7.25	1.50	46.1
medium	6	16	20	4.0	9.00	2.00	42.4
medium	6	18	22	5.0	10.00	2.00	47.7
medium	6	21	25	5.0	11.50	2.00	41.5
medium	6	23	28	6.0	12.75	2.50	44.9
medium	6	26	32	6.0	14.50	3.00	39.5
medium	6	28	34	7.0	15.50	3.00	43.1
medium	8	32	38	6.0	17.50	3.00	43.7
medium	8	36	42	7.0	19.50	3.00	45.7
medium	8	42	48	8.0	22.50	3.00	45.3
medium	8	46	54	9.0	25.00	4.00	45.8
medium	8	52	60	10.0	28.00	4.00	45.5
medium	8	56	65	10.0	30.25	4.50	42.1
medium	8	62	72	12.0	33.50	5.00	45.6

Three limits, the constants that are assumptions, and the factor of nine nobody mentions

A spline has three capacities and the smallest one is the answer. The teeth can shear off at the pitch line; the flanks can be crushed; and the shaft left underneath the teeth can twist off. They scale differently — the first two in proportion to the face width, the third not at all — so which one governs changes as soon as you change the length, and a calculation that checks only the teeth will happily bless a spline whose shaft is the weak link. This page computes all three and says which one won.

The constants in the published equations are assumptions, not safety factors. Darle Dudley’s 1957 paper is where these formulas come from, and he says plainly what they assume. The shear equation is S_s = 4T·K_m/(D·N·F_e·t_c), and the 4 is there because the constant “assumes that, because of spacing errors, only half the teeth carry the load” — to be raised to 6, a third of the teeth, with poor manufacturing accuracy. The bearing equation is S_c = 2T·K_m/(D·N·F_e·h), and there the constant 2 “assumes all teeth to be working, which becomes true after some initial wear”. Two equations for the same spline with two different assumptions about the same teeth — and both are right, because spacing errors decide which teeth shear on the first heavy load while wear eventually spreads the flank pressure over all of them. The fraction is an input on this page, and halving it doubles the shear stress and leaves the flank pressure alone.

The geometry is computable, and it was checked against a catalogue rather than assumed. Pitch diameter is N/P for a diametral-pitch spline and m·N for a module one; the circular tooth thickness at the pitch line is half the circular pitch, π/(2P). Those are consequences of what a pitch means. The one number that is not obvious is the radial height of flank actually in contact, and the default here is one addendum — which six published ANSI B92.1 shafts in Grob’s catalogue confirm to be exactly 0.5/P at two pitches and four tooth counts. It is the conservative reading: a side-fit spline’s real contact band also depends on the internal spline’s minor diameter, which is on your drawing. Enter it if you have it.

Fixed against flexible is a factor of nine, and crowned against straight is a factor of four. A fixed spline is a strength problem; a flexible one, allowed to move under load to accommodate misalignment, is a WEAR problem, and the allowable flank pressure drops accordingly. Dudley’s Eq (6) and Eq (7) put a factor of 8 on the flexible criterion and 9·K_a on the fixed one, and a second publisher states it in words: a fixed spline can carry nine times the compressive stress a flexible one can. Within the flexible case, crowning the teeth multiplies the allowable by exactly four at every row of his table. And the worst case is neither: a spline that is not deliberately flexible and not positively fixed either, which moves a few micrometres every revolution and fretting-corrodes. Dudley lists that as one of his five failure modes and it is the commonest way splines actually die — a flexible spline that is not lubricated does not wear, it welds, tears and generates its own abrasive.

What is refused. Two of Dudley’s five failure modes are not computed here. Tooth bending at the root needs the root geometry and a form factor that this batch could not source for the standard tooth forms; it is the mode that governs short coarse-pitch splines under shock, and guessing at it would be worse than naming it. Rupture of the internally toothed member is a hoop-stress problem in the hub wall and needs the hub’s outside diameter. Nor does this page apply a service factor for you — the torque you enter is the torque it uses. Key dimensions are on the parallel key and keyway dimensions calculator, the keyless alternative is on the interference fit and shrink fit calculator, and gear geometry belongs to the electronics side of this site, not here.

Frequently asked questions

How much torque can a spline carry?

The smallest of three numbers: the torque at which the teeth shear at the pitch line, the torque at which the flank pressure reaches its allowable, and the torque at which the shaft left under the teeth twists off. The calculator computes all three and reports which governs. At the defaults here — a 24-tooth 16/32 spline, 38 mm of face, fixed — flank bearing governs, and the answer changes to shaft torsion as soon as the face width grows.

Do all the spline teeth share the load?

No, and the published equations assume two different things about it on purpose. Dudley’s shear equation assumes only half the teeth carry, because of spacing errors; his flank-bearing equation assumes all of them do, because wear brings the rest into contact. One secondary source puts the load per tooth at up to four times the ideal, which is a quarter of the teeth. This page makes the fraction an input so you can see what it costs: halving it doubles the tooth shear stress and does not change the flank pressure at all.

What is the load distribution factor K_m?

Dudley’s multiplier for misalignment, between 1 and about 3, rising with both the misalignment and the face width — a wide spline concentrates its load at one end when the shafts are not parallel. Two published readings of his table are printed on this page side by side and they disagree in the middle rows, and modern finite-element work finds the table under-predicts K_m for long splines. So it is an input here, not a lookup. For a short spline on a rigid assembly, 1.0 is defensible; for anything wide or anything on separate bearings, it is not.

What is the difference between a fixed and a flexible spline?

A fixed spline cannot move on the shaft; a flexible one is allowed to, in order to accommodate misalignment. That changes the governing criterion from strength to wear, and the allowable flank pressure by a factor of about nine. Crowning the teeth of a flexible spline multiplies its allowable by four, because it keeps the contact in the middle of the face where it can roll rather than at the ends where it digs in. A flexible spline that is not lubricated fretting-corrodes, which is faster and nastier than ordinary wear.

Why is the shaft under the spline a separate limit?

Because cutting a spline removes material, so the torsional section is the minor diameter and not the nominal shaft size. Torsional capacity goes as the cube of the diameter, so a 10% reduction costs 27% of the capacity, and unlike the tooth limits it does not improve at all when you make the spline longer. It is Dudley’s failure mode (A) and it is the one that a spline calculation looking only at teeth cannot see. There is also a stress concentration where the spline ends, which this calculation does not include.

Can I use this for a DIN 5480 spline?

For the capacity, yes — the three limits are the same physics — but take the module and tooth count from the drawing and not from the designation. DIN 5480 names its splines by REFERENCE diameter, so a W 50 × 2 × 30 × 24 has a 50 mm reference diameter and a 48 mm pitch diameter, the difference being an addendum modification. ISO 4156, DIN 5480 and ANSI B92.1 also differ in tolerance and fit classes for the same nominal spline, which is exactly the kind of disagreement worth checking before you cut anything.

Which is better, a spline or a key?

A spline for torque and for reversing duty; a key for cost and for serviceability. A spline distributes the load over many teeth symmetrically, so it does not put a bending load into the shaft the way a single key does and it has no single stress raiser as severe as a keyway corner. It is also far more expensive to cut and it cannot be dismantled with a hammer and a drift. The honest middle ground for high torque without splines is an interference fit or a shrink disc, which has no stress concentration at all.

Related calculators

References

Darle W. Dudley. When Splines Need Stress Control, Product Engineering, 1957. The primary source for every formula on the spline page: the five failure modes (shaft breaks under the teeth, teeth shear at the pitch line, teeth break at the root, surfaces wear by fretting corrosion, the internally toothed shell ruptures); Eq (4) S_s = 4T·K_m/(D·N·F_e·t_c); Eq (5) S_c = 2T·K_m/(D·N·F_e·h); Eq (1) and (2) for the shaft under the spline; Table IV, the load distribution factor; and Table V, the allowable compressive stress. Dudley states the assumption behind the two constants explicitly: the 4 “assumes that, because of spacing errors, only half the teeth carry the load”, to be raised to 6 with poor manufacturing accuracy, while “the constant 2 in Eq (5) assumes all teeth to be working, which becomes true after some initial wear”.
Geepro Hobbing. Spline sizing and applications. The second published reading of Dudley’s method, used for two things. It gives a DIFFERENT K_m table from the one extracted from Dudley — both are printed on this page and neither is averaged — and it states the fixed-against-flexible ratio in words: “fixed spline can carry 9 times more compressive stresses than flexible spline”, which matches Dudley’s Eq (6) and (7). Its printed chordal thickness “t_e ≈ D/2N” is short by a factor of π; the correct half-circular-pitch value is πD/2N, and the force balance behind Dudley’s Eq (4) confirms which is meant.
Gear Solutions. “Filling Some Gaps in Spline Design Guidelines: Centering, Friction, and Misalignment.” The modern finite-element check on Dudley’s Table IV, and it does not vindicate it: “Dudley’s table of misalignment factors is shown to under-predict the misalignment factor for some long L/D splines”, with the data falling into two patterns, a power function at L/D = 1.0 and near-linear at L/D = 0.2. Cited as the reason this page lets you enter K_m yourself.
Grob Inc. ANSI B92.1 Spline Shafts catalogue listing. The source that lets this page compute the involute geometry instead of tabulating it: six published shafts, from 30-16/32-9 to 30-12/24-20, whose outside diameters put the external spline’s addendum at exactly 0.5/P at every row — 0.031250 in at 16/32 and 0.041667 in at 12/24 — once the pitch diameter is taken as N/P. Nothing was fitted to them.
ANSI B92.1 (and its metric-module companion ANSI B92.2M), Involute Splines and Inspection, with SAE J498 and ISO 4156 / DIN 5480 as the other families. Cited by number; not fetched. The three relations this page uses from the definition are the pitch diameter D = N/P, the circular pitch p = π/P and the basic circular tooth thickness at the pitch line p/2 = π/(2P) — all three arithmetic consequences of what a diametral pitch means. DIN 5480’s designation is by REFERENCE diameter rather than pitch diameter, so a DIN 5480 spline’s m·z is not the number in its name; that family is named on the page and its geometry is not computed here.
RoyMech. ISO Straight Sided Spline (BS 5686:1986, ISO 14-1982) and Key and Spline Strength Calculations. The source for the twenty-five light- and medium-series straight-sided spline sizes, and for the conventional straight-spline capacity form. Its involute formulas assume every tooth carries load, which is the assumption Dudley’s constant 4 exists to reject.