Free tool · inch and metric

Bolt torque calculator.

Pick a thread, a grade, a nut factor and a target preload, and get the clamp force and the tightening torque, with the working shown. Strengths come from our grade pages; the formulas are the standard ones, written out below.

Thread size

Grade

Nut factor K

Target preload, % of strength

of minimum yield strength of proof load stress (not given for this grade)

795

Torque, ft·lbf · 1,078 N·m

47,699

Preload, lbf · 212 kN

Working

Tensile stress area: As = 0.7854 × (D − 0.9743 / n)² = 0.6057 sq in.

ASTM A193 B7, 2½ and under: minimum yield strength 105 ksi (105,000 psi) (grade data)

Preload: F = 75% × 105,000 psi × 0.6057 sq in. = 47,699 lbf

Torque: T = K × D × F = 0.20 × 1 in.× 47,699 lbf ÷ 12 = 795 ft·lbf

An estimate, not a specification. K varies with finish, coating, lubricant, washers and tightening method, so the same torque can give very different preloads. Verify against your joint design, the gasket or equipment maker's figures, or a test on the actual parts.

How it works

Preload first, then torque.

A bolt holds a joint by being stretched, and the clamp force that stretch creates is the preload. The calculator works out the preload you asked for, then the torque that should produce it.

1. Stress areaInch (ASME B1.1): A_s = 0.7854 × (D − 0.9743 / n)², with D the nominal diameter in inches and n the threads per inch.
Metric (ISO 898-1): A_s = 0.7854 × (d − 0.9382 P)², with d the nominal diameter and P the pitch, in mm.

2. PreloadF = target % × S × A_s, where S is the grade's minimum yield strength or, where the grade gives one, its proof load stress, for that diameter.

3. TorqueT = K × D × F. Inch: D in inches and F in lbf, divided by 12 for ft·lbf. Metric: d in mm and F in N, divided by 1000 for N·m.

Units1 lbf = 4.44822 N · 1 ft·lbf = 1.35582 N·m · 1 ksi = 6.89476 MPa

Nut factor

Typical K values.

K changes the answer more than anything else. These are typical, approximate starting points, not guarantees; use the value your lubricant maker publishes, or measure it.

Dry steelAbout 0.20 for plain, as-received steel. A common default.

Lightly oiledAbout 0.18.

LubricatedAbout 0.15 with oil or anti-seize; depends on the product.

Moly pasteAbout 0.12 with molybdenum disulfide paste; depends on the product.

Coated partsZinc, hot-dip galvanized and other coatings can differ a lot from bare steel, dry galvanized often higher. Use the coater's or lubricant maker's value, or test.

Worked examples

Example torque charts.

The same calculation run for every size of two common grades, at 75 percent of minimum yield. Change the grade, K or target in the calculator above for your own case. Coated or lubricated bolts need the K for that condition.

Example torque chart: ASTM A193 B7, UNC threads, 75% of minimum yield

Thread	As (sq in.)	Yield, min	Preload at 75% (lbf)	Torque, K = 0.20		Torque, K = 0.15
Thread	As (sq in.)	Yield, min	Preload at 75% (lbf)	ft·lbf	N·m	ft·lbf	N·m
1/4"-20 UNC	0.0318	105 ksi	2,504	10.4	14.1	7.83	10.6
5/16"-18 UNC	0.0524	105 ksi	4,127	21.5	29.1	16.1	21.9
3/8"-16 UNC	0.0775	105 ksi	6,103	38.1	51.7	28.6	38.8
7/16"-14 UNC	0.1063	105 ksi	8,371	61.0	82.8	45.8	62.1
1/2"-13 UNC	0.1419	105 ksi	11,175	93.1	126	69.8	94.7
9/16"-12 UNC	0.1819	105 ksi	14,325	134	182	101	137
5/8"-11 UNC	0.2260	105 ksi	17,798	185	251	139	189
3/4"-10 UNC	0.3345	105 ksi	26,342	329	446	247	335
7/8"-9 UNC	0.4617	105 ksi	36,359	530	719	398	539
1"-8 UNC	0.6057	105 ksi	47,699	795	1,078	596	808
1-1/8"-7 UNC	0.7633	105 ksi	60,110	1,127	1,528	845	1,146
1-1/4"-7 UNC	0.9691	105 ksi	76,317	1,590	2,156	1,192	1,617
1-3/8"-6 UNC	1.1549	105 ksi	90,948	2,084	2,826	1,563	2,119
1-1/2"-6 UNC	1.4053	105 ksi	110,667	2,767	3,751	2,075	2,813
1-3/4"-5 UNC	1.8995	105 ksi	149,586	4,363	5,915	3,272	4,436
2"-4.5 UNC	2.4982	105 ksi	196,733	6,558	8,891	4,918	6,668
2-1/4"-4.5 UNC	3.2477	105 ksi	255,756	9,591	13,003	7,193	9,753
2-1/2"-4 UNC	3.9988	105 ksi	314,906	13,121	17,790	9,841	13,342
2-3/4"-4 UNC	4.9340	95 ksi	351,548	16,113	21,846	12,084	16,384
3"-4 UNC	5.9674	95 ksi	425,177	21,259	28,823	15,944	21,617
3-1/4"-4 UNC	7.0989	95 ksi	505,797	27,397	37,146	20,548	27,859
3-1/2"-4 UNC	8.3286	95 ksi	593,413	34,616	46,933	25,962	35,199
3-3/4"-4 UNC	9.6565	95 ksi	688,026	43,002	58,302	32,251	43,727
4"-4 UNC	11.0826	95 ksi	789,635	52,642	71,373	39,482	53,530

Calculated with this page's formulas: B7 minimum yield 105 ksi to 2-1/2 in. and 95 ksi over 2-1/2 to 4 in. (ASTM A193). Estimates only; K = 0.20 is a typical dry-steel value and 0.15 a typical lubricated value. Use the K for your finish and lubricant.

Example torque chart: property class 10.9, metric coarse threads, 75% of minimum yield

Thread	As (mm²)	Yield, min	Preload at 75% (kN)	Torque, K = 0.20		Torque, K = 0.15
Thread	As (mm²)	Yield, min	Preload at 75% (kN)	N·m	ft·lbf	N·m	ft·lbf
M5 × 0.8	14.2	940 MPa	10.0	10.0	7.38	7.51	5.54
M6 × 1	20.1	940 MPa	14.2	17.0	12.5	12.8	9.41
M8 × 1.25	36.6	940 MPa	25.8	41.3	30.5	31.0	22.8
M10 × 1.5	58.0	940 MPa	40.9	81.8	60.3	61.3	45.2
M12 × 1.75	84.3	940 MPa	59.4	143	105	107	78.9
M14 × 2	115.4	940 MPa	81.4	228	168	171	126
M16 × 2	156.7	940 MPa	110	354	261	265	196
M18 × 2.5	192.5	940 MPa	136	489	360	366	270
M20 × 2.5	244.8	940 MPa	173	690	509	518	382
M22 × 2.5	303.4	940 MPa	214	941	694	706	521
M24 × 3	352.5	940 MPa	249	1,193	880	895	660
M27 × 3	459.4	940 MPa	324	1,749	1,290	1,312	967
M30 × 3.5	560.6	940 MPa	395	2,371	1,749	1,779	1,312
M33 × 3.5	693.6	940 MPa	489	3,227	2,380	2,420	1,785
M36 × 4	816.7	940 MPa	576	4,146	3,058	3,109	2,293
M39 × 4	975.8	940 MPa	688	5,366	3,958	4,024	2,968
M42 × 4.5	1120.9	940 MPa	790	6,638	4,896	4,978	3,672
M45 × 4.5	1306.0	940 MPa	921	8,287	6,112	6,215	4,584
M48 × 5	1473.2	940 MPa	1,039	9,971	7,354	7,478	5,515
M52 × 5	1757.8	940 MPa	1,239	12,888	9,506	9,666	7,129
M56 × 5.5	2030.0	940 MPa	1,431	16,029	11,822	12,022	8,867
M60 × 5.5	2362.0	940 MPa	1,665	19,983	14,738	14,987	11,054
M64 × 6	2676.0	940 MPa	1,887	24,148	17,811	18,111	13,358

Calculated with this page's formulas: class 10.9 minimum yield 940 MPa (ISO 898-1 / ASTM F568M). Estimates only; use the K for your finish and lubricant.

Questions

Bolt torque: common questions.

How do you calculate bolt torque?

With the short-form torque equation T = K × D × F: T is the tightening torque, K the nut factor, D the nominal bolt diameter and F the preload (clamp force) you want. Pick the preload first, usually as a percentage of the bolt's minimum yield or proof strength times its tensile stress area, then multiply by K and D. In inch units divide by 12 to get ft·lbf; in metric, with d in mm and F in newtons, divide by 1000 to get N·m.

What is the nut factor K?

K is an experimental factor that lumps together thread friction, friction under the nut or head, and the thread geometry. It is not a pure friction coefficient. Dry, as-received steel is often taken as about 0.20; lubricants bring it down, typically to somewhere around 0.10 to 0.18 depending on the product. The best value is the one your lubricant maker publishes or one measured on the actual parts.

What preload should I tighten a bolt to?

That is set by the joint design. Many bolted joints target roughly 50 to 75 percent of the bolt's minimum yield strength; flanged joints follow the bolt stress set by the designer, the gasket maker or a standard such as ASME PCC-1. This calculator defaults to 75 percent of minimum yield and lets you change it.

Why does lubrication change the torque so much?

Most of the torque you apply goes into overcoming friction, so only a small part stretches the bolt. Lower friction means more of the same torque becomes preload. Using a dry-steel torque on a lubricated bolt can overload it, which is why the K you use must match the actual finish and lubricant.

Does this work for stud bolts with two nuts?

Yes. Use the stud's nominal diameter and thread and the K for the nut face and threads you will tighten. The torque is applied at the nut.

Why is a grade marked 'not listed for this size'?

Strength requirements change with diameter and some grades only cover certain sizes. The calculator uses only the size ranges printed on our grade pages, so a size outside them is not given a number. For example, our data for property class 8.8 covers M20 and up.

How accurate is a torque calculation?

It is an estimate. Friction varies from part to part and with coatings, lubricants, washers and tightening speed, so preload achieved by torque alone can easily vary by 25 percent or more. Where preload is critical, use tensioning, direct tension indicators, ultrasonic measurement or a torque-tension test on the actual parts.

Estimates only, with no guarantee. The nut factor varies with finish, coating, lubricant, washers and tightening method; verify any torque against your joint design, the equipment or gasket maker's instructions, or a test on the actual parts. Strength values are specification minimums from our grade pages; thread sizes and stress areas follow ASME B1.1 and ISO 898-1.

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Bolt torque calculator.

Preload first, then torque.

Typical K values.

Example torque charts.

Bolt torque: common questions.

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Need the bolts or studs themselves?