Bearing Equivalent Load Calculator

P = X·F_r + Y·F_a, with the limit e that X and Y switch at — and with e itself moving as F_a/C₀ changes on a deep groove bearing. Plus the thrust a taper pair makes for itself, the static safety factor and the minimum load.

Last updated 24 Sep 2026

Bearing equivalent dynamic load

F_r, F_a, C₀ → equivalent load P

Bearing familyX, Y and the limit e all belong to the bearing family, and for a deep groove or 15° angular contact bearing they also move with F_a/C₀. A plain cylindrical roller bearing takes NO axial load at all, which is the trap this page exists for.

Radial load F_r (N)The load perpendicular to the shaft. A belt or chain pull is a radial load; so is the weight of everything the shaft carries and the separating force of a gear mesh.

External axial load F_a (N)The load along the shaft, from outside the bearing. A helical gear’s thrust, a fan or pump’s hydraulic thrust, a belt pulled off-centre. Do NOT put a taper pair’s own induced thrust here — the page adds that separately.

Basic static load rating C₀ (kN)The catalogue’s C₀ or C_0r. It does two jobs here: it sets e and Y for a deep groove or 15° angular contact bearing, and it is the numerator of the static safety factor.

Basic dynamic load rating C (kN)Only used for the minimum load check and to let you take the answer straight to the life page.

Catalogue Y for a tapered roller bearingA per-designation catalogue value, typically 1.4 to 1.9 for a metric single row taper. The limit e follows from it: e = 0.6/Y, which reproduces the catalogue’s own printed e to about one per cent. Also used for the induced thrust.

ArrangementA tapered roller or angular contact bearing generates an axial load out of a radial one, so in an opposed pair the OTHER row’s induced thrust arrives at this one and has to be added to the external axial load. That is the classic taper roller mistake.

Radial load on the opposed row F_rB (N)Only used when you have selected an opposed pair. The induced thrust it sends this way is 0.5·F_rB/Y.

Not a circuit: two straight segments and the kink between them, drawn in normalised coordinates so that one figure serves every bearing family. The horizontal axis is the axial load in units of e·F_r — so the switch always happens at 1 — and the vertical axis is the equivalent load in units of F_r. Below the switch the line is flat at P = F_r: the axial load is free. Above it the line slopes, and in these coordinates its gradient is exactly (1 − X), which is why the curve changes when you change the bearing family and why the two branches meet rather than jump. A cylindrical roller bearing is the flat line that never kinks, and a thrust ball bearing is the straight line from the origin. The faint extensions on the deep groove family show each branch carried past the switch: the sloping branch alone would understate the load below e, which is what the flat branch is for. Below, the opposed taper pair in section: each row turns its radial load into an axial one of 0.5·F_r/Y, and row A carries row B's induced thrust PLUS the external load.

4,581.7NExample

A deep groove ball bearing with C₀ = 19 kN carrying 4,000 N radially and 1,500 N axially, on its own

The equivalent load, the switch at e, and the thrust a taper pair makes for itself

P = F_r when F_a/F_r ≤ e · P = X·F_r + Y·F_a when F_a/F_r > e · X + Y·e = 1 · F_a,induced = 0.5·F_r/Y · P₀ = X₀·F_r + Y₀·F_a · s₀ = C₀/P₀

P: equivalent dynamic load — the single radial load that would do the same fatigue damage as the real combination. It is what the life page needs
e: the limit at which the axial load starts to count. For a deep groove or 15° angular contact bearing it MOVES with F_a/C₀, which is why this needs its own page
X, Y: radial and axial factors, used only above e. Below e they are 1 and 0, so P = F_r and the axial load is free
X + Y·e = 1: not a coincidence: the two branches of P must agree where they meet. It pins Y from X and e and it is a free check on any table you look up
0.5·F_r/Y: the axial load a tapered roller or angular contact row generates out of its own radial load. In an opposed pair it arrives at the other row
P₀, s₀: static equivalent load and static safety factor. A separate check against permanent denting of the raceway, using the PEAK load

Worked example

A deep groove ball bearing with C₀ = 19 kN carrying 4,000 N radially and 1,500 N axially, on its own
The order of operations is the trap. You cannot look up X and Y until you know e, and e depends on the axial load you are trying to apply. So start there: F_a/C₀ = 1,500/19,000 = 0.07895
Read e and Y against that. Between the published rows at 0.07 (e = 0.27, Y = 1.6) and 0.13 (e = 0.31, Y = 1.4), interpolating gives e = 0.2778 and Y = 1.5611, with X = 0.56 throughout the table. Check them against each other before going on: X + Y·e = 0.9936, which is 1 to within half a per cent, as it must be
Now decide which branch you are on. F_a/F_r = 1,500/4,000 = 0.3750, and e is 0.2778. The ratio is ABOVE e, so the axial load counts and the second branch applies. Had the axial load been 1,111 N or less it would have been free: P would have been exactly 4,000 N
P = X·F_r + Y·F_a = 0.56 × 4,000 + 1.561 × 1,500 = 2,240 + 2,342 = 4,582 N. So the 1,500 N of thrust has cost you 582 N of equivalent load, which is 14.5 per cent — and through the cube law on the life page that is 33 per cent of the life
The static check is separate and must not be skipped. P₀ = 0.6F_r + 0.5F_a = 2,400 + 750 = 3,150 N, which is LESS than the radial load, so the floor applies and P₀ = F_r = 4,000 N. Then s₀ = C₀/P₀ = 19,000/4,000 = 4.75, comfortably above the 1 that normal running wants and above the 2 that quiet running wants. Remember to use the PEAK load here, not the running one
And the minimum load, which is the check nobody makes. 0.02·C = 0.02 × 32,500 = 650 N, and P is 4,582 N, so this bearing is loaded enough to roll rather than skid. The two published minimum-load rules disagree by a factor of three, so this is an amber flag rather than a specification
If this bearing were one row of an opposed TAPER pair with Y = 1.6 and the other row carrying 2,500 N radially, that row would send 0.5 × 2,500/1.6 = 781.3 N of induced thrust this way, on top of the external 1,500 N. Forgetting that term is the classic tapered roller error, and it is always in the unsafe direction

Deep groove ball bearings: e and Y move with F_a/C₀

This is the double dependence that earns this page its own URL. X and Y switch at the limit e — and e itself is not a constant: it moves with the axial load as a fraction of the STATIC rating, from 0.22 to 0.44 across the table. So you cannot look up X and Y until you know F_a, and the answer feeds back on itself. The fifth column is the free check. The two branches of P = X·F_r + Y·F_a must give the same answer where they meet, at F_a/F_r = e, which forces X + Y·e = 1 exactly. Every row satisfies it to better than one per cent, and the last row exactly. That identity is not decoration: three separate summarised readings of this table during this batch’s research came back with a column shifted — one lost X entirely, one moved e down a row — and the identity is what caught each of them. The sixth column shows the same thing from the other side: given X and e, Y is determined. 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.
F_a/C₀	e	X	Y	X + Y·e	(1−X)/e
0.025	0.22	0.56	2.00	1.0000	2.000
0.040	0.24	0.56	1.80	0.9920	1.833
0.070	0.27	0.56	1.60	0.9920	1.630
0.130	0.31	0.56	1.40	0.9940	1.419
0.250	0.37	0.56	1.20	1.0040	1.189
0.500	0.44	0.56	1.00	1.0000	1.000

X, Y and e by bearing family — and which can take thrust

Below e, every one of these has X = 1 and Y = 0, which is to say P = F_r and the axial load is free. That is the part people miss: a modest axial load on a deep groove ball bearing costs nothing at all, and only once F_a/F_r passes e does it start to count. Above e the contact angle is what decides the numbers, and the trend is consistent — a steeper contact angle takes more thrust per newton of capacity (Y falls from 2.0 to 0.57) and tolerates more thrust before the switch (e rises from 0.22 to 1.14). The cylindrical roller row is the one to remember. Fitting a plain cylindrical roller bearing at each end of a helical pinion leaves the thrust nowhere to go and the shaft walks — and a helical gear’s thrust is F_t·tan β, which at a 20° helix is 36 per cent of the tangential force and not a detail. 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.
Family	e	X (above e)	Y (above e)	Takes axial load?
Deep groove ball	0.22 – 0.44, with F_a/C₀	0.56	1.0 – 2.0	Yes, modestly. Roughly a quarter to a half of its radial rating, and only with enough radial load to keep the balls seated
Angular contact ball, 15°	0.38 – 0.56, with F_a/C₀	0.44	1.00 – 1.46	Yes, in ONE direction only. Mount it against something
Angular contact ball, 25°	0.68	0.41	0.87	Yes, more than the 15°, and the switch comes later
Angular contact ball, 30°	0.80	0.39	0.76	Yes. Note e = 0.80: the axial load has to reach eighty per cent of the radial one before Y is used at all
Angular contact ball, 40°	1.14	0.35	0.57	Heavily, and e is above 1 — an axial load smaller than the radial one does not change P at all
Cylindrical roller, plain	no limit	1	0	NONE. Not a small amount: none. It is the bearing with the highest radial capacity of the group and it cannot take a newton of thrust
Tapered roller, single row	0.6/Y, about 0.31 – 0.43	0.4	1.4 – 1.9, from the catalogue	Heavily, in one direction, and it MAKES ITS OWN from the radial load
Thrust ball	—	0	1	Only axial. A radial load on a thrust ball bearing is not a load case, it is a mistake

Tapered roller bearings: the catalogue Y, and the thrust the bearing makes for itself

Two things to take from this table. First, e and Y are not independent: the continuity of P forces 0.4 + Y·e = 1, so e is 0.6/Y, and the seventh column reproduces the catalogue’s own printed e to within two per cent at every designation. If you have Y you have e. Second, the last column is the reason a taper pair needs care. A single row under a radial load generates its own axial load of 0.5·F_r/Y, which is an F_a/F_r of 0.5/Y — and since e is 0.6/Y, that self-generated thrust always sits just BELOW the bearing’s own switching limit, by exactly the ratio of the two constants. That is not a coincidence: it is why a row of a pair that carries only its own induced thrust can be treated as radially loaded, with P = F_r. The row that is actually loaded gets the other row’s induced thrust PLUS the external one, and that sum is what this page adds up. 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. 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.
Designation	d (mm)	D (mm)	T (mm)	Catalogue e	Catalogue Y	0.6/Y	0.4 + Y·e	Induced F_a/F_r = 0.5/Y
30204	20	47	15.25	0.35	1.70	0.353	0.9950	0.2941
30206	30	62	17.25	0.37	1.60	0.375	0.9920	0.3125
30208	40	80	19.75	0.37	1.60	0.375	0.9920	0.3125
30210	50	90	21.75	0.43	1.40	0.429	1.0020	0.3571
30306	30	72	20.75	0.31	1.90	0.316	0.9890	0.2632
32206	30	62	21.25	0.37	1.60	0.375	0.9920	0.3125
32208	40	80	24.75	0.37	1.60	0.375	0.9920	0.3125

Static safety factor s₀ = C₀/P₀: recommended minimums

The static check is a different question from the life calculation and it has to be asked separately. C₀ is the load that produces a stated contact stress at the most heavily loaded rolling element, and exceeding it dents the raceway permanently — which then makes noise and vibration for the rest of the bearing’s life, whatever the fatigue calculation said. Note that roller bearings want higher factors than ball bearings for the same duty, and that the shock-load figures are the ones that catch people: the load to use in P₀ is the PEAK load, including the shock, not the working load. A crane hook stopping, a press at bottom dead centre and a gearbox starting against a locked output are all static load cases that have nothing to do with the running load. 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.
Condition	Minimum s₀
Ball bearing, quiet running wanted	2.0
Ball bearing, normal running	1.0
Ball bearing, shock loaded	1.5
Roller bearing, quiet running wanted	3.0
Roller bearing, normal running	1.5
Roller bearing, shock loaded	3.0

The switch at e, the identity that checks it, and the thrust a taper pair makes for itself

X and Y switch at a limit e, and on the commonest bearing of all, e is not a constant. The equivalent load is P = X·F_r + Y·F_a, with X = 1 and Y = 0 while F_a/F_r stays below e — which is to say a modest axial load is FREE. Above e the axial load starts to count. For a deep groove ball bearing, and for a 15° angular contact one, the limit e itself moves with F_a/C₀, running from 0.22 to 0.44 across the published table. So you cannot look up the factors until you know the axial load, and the answer depends on the table row the answer picks. That double dependence is why this needs its own page rather than a line on the life page.

There is a free check on every one of these tables and it is X + Y·e = 1. The two branches of P have to agree where they meet, at F_a/F_r = e, so 1 = X + Y·e identically. Across thirty-one published rows — six deep groove, nine in the f₀ form of the same table, six angular contact at 15°, three at fixed contact angles and seven tapered roller designations — it holds to better than 1.6 per cent everywhere and exactly where Y = 1. Use it. During this batch’s research three separate summarised readings of the deep groove table came back with a column shifted — one lost X entirely, one moved e down by a row, and they disagreed with each other — and the identity is what identified the correct reading in each case. If a table you have looked up fails it by more than a couple of per cent, you have read a row wrong.

A tapered roller pair makes its own axial load, and the second row’s arrives at the first. Any bearing with a non-zero contact angle turns a radial load into an axial one: for a taper row it is 0.5·F_r/Y. In an opposed pair the two induced loads do not cancel, they balance — and the row that the external load pushes towards carries the OTHER row’s induced thrust plus the external one. Leaving that term out is the classic tapered roller mistake and it is always in the unsafe direction. There is a neat consistency worth noticing: since e = 0.6/Y, a row carrying only its own induced thrust has F_a/F_r = 0.5/Y, which sits just BELOW its own limit e — by exactly the ratio 5/6. That is why the lightly loaded row of a pair can be treated as radially loaded.

A plain cylindrical roller bearing takes no axial load at all. Not a little: none. It has the highest radial capacity of any of these families and, without flanges, nothing for a thrust to push against. Fit one at each end of a helical pinion and the thrust has nowhere to go. NJ and NUP designs add a flange and take some axial load as a SLIDING contact, at a capacity the maker states separately and which is far below the radial rating. At the other end of the range, a 40° angular contact bearing has e = 1.14, which is a statement that it expects the axial load to be the larger of the two.

Two checks that are not the life calculation. The static safety factor s₀ = C₀/P₀ asks whether the PEAK load will dent the raceway permanently, which is a question about contact stress and not about fatigue; ISO 76 defines it and the recommended minimums are 1 for normal running and 2 for quiet running on a ball bearing, 1.5 and 3 on a roller bearing. And the MINIMUM load asks whether the bearing is loaded enough to roll rather than skid, because a bearing run too lightly smears its raceways and dies faster than an overloaded one. The two published minimum-load rules — 0.02·C and 0.01·C₀ — differ by about a factor of three, so both are printed here and neither is offered as a specification. Once P is settled, take it to the L10 life page.

Frequently asked questions

Why does e change with the axial load?

Because e marks where the ball-to-raceway contact has climbed far enough up the groove for the contact angle to have changed materially, and how far it climbs depends on how hard it is pushed relative to the bearing’s static capacity. That is why the published table’s abscissa is F_a/C₀ (or f₀F_a/C₀, which is the same thing with a per-bearing calculation factor folded in) and not F_a alone. The practical consequence is that you read the table against the axial load, then check the branch, and the two steps are in that order.

What is the identity X + Y·e = 1 for?

It is a free check on any X/Y/e table you look up, and it costs nothing. The equivalent load has two branches that must give the same answer at the point where they meet, F_a/F_r = e: the lower branch gives F_r and the upper gives X·F_r + Y·e·F_r, so X + Y·e must be 1. Every published row checked in building this page satisfies it to better than 1.6 per cent. If a row you have read fails it badly, you have taken a value from the wrong column — which, in tables printed as images and summarised by machines, is common.

Do I add the induced axial load of a taper pair to the external one?

Yes, on the row that the external axial load pushes towards, and that row’s axial load is 0.5·F_rB/Y_B + F_external where row B is the OTHER one. The other row then carries only its own induced thrust, which — because e = 0.6/Y and the induced ratio is 0.5/Y — sits just below its own limit e, so it is treated as radially loaded with P = F_r. Forgetting the induced term understates the load on the working row, and through the cube law that understates the life by much more.

Can a cylindrical roller bearing take any axial load?

A plain one, with no flanges, takes none at all — and it is the family with the highest radial capacity, which is exactly why the mistake gets made. NJ (one flanged ring) and NUP (two) designs do take axial load, but as a sliding contact between the roller end and the flange rather than as a rolling contact, so the permissible axial load is a separate and much smaller figure that the maker states with its own speed and lubrication conditions. If you need real axial capacity with roller radial capacity, that is a tapered roller pair.

What is the minimum load a bearing needs?

Enough to make the rolling elements roll rather than skid. Two published rules are printed on this page and they disagree by about a factor of three: American Roller Bearing gives P_min = 0.02·C for ball, cylindrical and spherical roller bearings, and NTN-SNR gives 0.01·C₀ for spherical rollers. Both are rules of thumb standing in for formulas that depend on speed, lubricant viscosity and bearing size, and every major maker publishes one. What matters is that the failure mode exists at all: too little load causes skidding and smearing, which is faster and nastier than fatigue.

Is the static safety factor the same as a factor of safety on the life?

No. It is a different failure mode entirely. s₀ = C₀/P₀ asks whether the peak load will permanently dent the raceway — plastic deformation at the contact, not fatigue — and it uses the PEAK load, including shock, starting torque, and anything that happens while the shaft is stationary. A bearing can have a perfectly adequate L10 and still be destroyed by a single shock load, and the dents then become the fatigue initiation sites for the rest of its life. ISO 76 is the governing document.

Which X, Y and e apply to a self-aligning ball bearing or a spherical roller bearing?

Values that this page deliberately does not print, because they vary by series in a way a single row cannot capture and this batch could not obtain them from two independent sources. For a self-aligning ball bearing X and Y depend on the series (the ratio of the ball set’s pitch diameter to the bore), and for a spherical roller bearing they depend on the internal design; in both cases the maker prints them per designation in the same column as C and C₀. The structure of the calculation is identical to the ones here, and the identity X + Y·e = 1 will check whatever values you look up.

Related calculators

References

NTN, Ball and Roller Bearings, catalogue 2203-E, section B-17, “Deep Groove Ball Bearings”. The source for the f₀F_a/C_0r form of the X/Y/e table and for P_0r = 0.6F_r + 0.5F_a. NOTE: the summarised fetch of this page returned the table with its X column absorbed into Y — X = 0.56 appeared only in the first row and every Y was one cell to the left. A second printing of the same table (Koyo) came back shifted a different way, with the e column moved down one row. What settled it was the identity the table has to satisfy, X + Y e = 1; see the page.
NACHI, Angular Contact Ball Bearings dimension tables and load factor section. The source for the fixed contact angle rows (e = 0.68/0.80/1.14 with X = 0.41/0.39/0.35 and Y = 0.87/0.76/0.57 at 25°, 30° and 40°) and for the static factors Y₀ = 0.46/0.33/0.26. All three dynamic rows satisfy X + Y e = 1 to within 0.2 per cent.
Two independent printings of the single row angular contact ball bearing e/X/Y tables: a Dunlop/BTL catalogue section and URB’s single row angular contact catalogue. They disagreed: the first returned a Y column 12.2 per cent higher than the second at every row, uniformly. The second’s columns satisfy 0.44 + Y e = 1 and the first’s do not, and the constant ratio identifies the first as the matched-pair Y₁ column read under the single-row heading. The identity-consistent set is the one used.
A distributor printing of the metric single row taper roller bearing tables (30200, 30300 and 32200 series) with the e and Y calculation-factor columns. The seven designations printed on this page are taken from it, and every one of them satisfies 0.4 + Y e = 1 to better than 1.1 per cent, which is what makes the reading trustworthy. The same source gives the single row equations P = F_r below e and P = 0.4F_r + YF_a above it.
PEER Bearing, Tapered Roller Bearings (published catalogue preview). The source for the induced axial load in the form this page uses, F_aA = 0.5 F_rB/Y_B + F_ea — that is, the axial load on the loaded row of a pair is the OTHER row’s induced load plus the external one.
Power Transmission Engineering, “Induced axial load”. Cited for the physical statement rather than a number: “every bearing that has a non-zero contact angle will generate an axial load as a radial load is applied”, and that on a pair connected by a solid shaft the two induced loads do not cancel but balance, so the larger one becomes the shaft’s axial load.
NES Bearings, Calculating static safety factor — ISO 76. The source for the recommended minimum s₀ values: 2, 1 and 1.5 for ball bearings and 3, 1.5 and 3 for roller bearings, for quiet running, normal running and shock loading respectively.
ISO 76:2006, Rolling bearings — Static load ratings. Cited by number. It defines the basic static load rating C₀ as the load producing a stated contact stress at the most heavily loaded rolling element, and the static equivalent load P₀ as the load that would produce the same stress. The static safety factor s₀ = C₀/P₀ and its recommended minimum values are taken from NES Bearings’ published ISO 76 note, attributed where they appear.
American Roller Bearing, Bearing Life Calculation — Bearing Loads & Speeds. The source for the minimum load rule P_min = 0.02C and for a second, independent printing of the ISO 281:2007 a₁ column. NOTE: its own life equation is printed as L₁₀ = (C/P)^e × 10⁶/N, which is a life in MINUTES, not hours — the factor of 60 is missing. Recorded because it is the commonest slip on this calculation and it is a factor of sixty.
Bartlett Bearing, Understanding minimum load requirements for bearings. Cited for the failure mechanism in its own words — too little load makes “rolling elements slide rather than roll, a condition called skidding”, which “disrupts the lubrication film, leading to smearing”, and can leave the cage driving the elements rather than being driven by them. It gives no numbers, which is why the two numeric rules on the page come from elsewhere and are both named.
Schaeffler, product datasheet for a 6001-C-2HRS deep groove ball bearing. Cited for one number: the calculation factor f₀ = 13.1, which is what makes the two published forms of the deep groove X/Y/e table — one with F_a/C₀ as its abscissa and one with f₀F_a/C_0r — the same table. It is also the reminder that f₀ is a per-bearing catalogue value and not a constant.