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Bolt Torque Calculator

Estimate how much torque to tighten a bolt to for the clamp load you want, using T = K × D × F. Enter the clamp load, or set it as a percentage of proof load.

Level: Grades 6–7

  • Common Core standard 6.EE.A.2.cEvaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
  • Common Core standard 7.RP.A.3Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Printable worksheet

Bolt Torque Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Thread system
Clamp load from

75% of proof load is a widely used starting target for joints you may take apart again. Joint designers may choose differently.

K bundles together the friction in the threads and under the head. Lubricants and platings change it a lot.

Result

Estimated tightening torque

75.4 lbf·ft

About 75.4 lbf·ft to reach 9,046 lbf of clamp load with K = 0.2. Use the manufacturer's torque spec where one exists.

Clamp load (preload)
9,046 lbf
Nut factor used
0.2
Tensile stress area
0.1419 in²
Proof load
12,061 lbf
In newton meters
102.2 N·m
In kilonewton meters
0.1 kN·m
In pound-force inches
904.6 lbf·in

See the step-by-step solution ↓

Step-by-step solution

  1. Find the bolt's effective cross-section through the threads (tensile stress area) for 1/2-13 UNC. D is the diameter: (π/4) × (D − 0.9743 × pitch)²

    π4×(0.5−0.9743×0.07692308)2=0.141898 in²

  2. Find the proof load, the most the bolt can hold without stretching for good: proof strength × stress area

    85,000 psi×0.141898 in²=12,061.371872 lbf

  3. Set the clamp load you're aiming for: 75% of the proof load

    12,061.371872 lbf×75%=9,046.028904 lbf

  4. Find the tightening torque T: nut factor K × bolt diameter D × clamp load F

    0.2×0.5 in×9,046.028904 lbf=904.60289 lbf·in

  5. Convert to lbf·ft

    904.60289 lbf·in×0.0833333333=75.383574 lbf·ft

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Get a planning estimate of how tight to make a bolt for the clamping force you want. A tightened bolt stretches a tiny bit, like a stiff spring. That tension, called preload, squeezes the parts together. Tension is hard to measure, so people usually set it by tightening to a torque (a twisting force). The short-form torque equation links the two: T = K × D × F. T is the torque. K is the nut factor, D is the bolt's nominal (labeled) diameter, and F is the clamp load. K bundles together the friction in the threads and under the head. That friction uses up most of the torque you apply.

Choose a UNC, UNF or metric bolt. Then enter the clamp load you need, or let the calculator set it as a percentage of the bolt's proof load. It works that out from the bolt's SAE grade or ISO property class. You'll see the tensile stress area, proof load, preload and estimated torque. This is a planning estimate only. For head bolts, wheel lug nuts, suspension, brakes, structural connections and anything else critical, always use the maker's torque spec and procedure. That means the vehicle, equipment or fastener manufacturer.

Where it's used

Why this math matters outside the classroom:

  • Machine assembly. A millwright estimates 0.2 × 0.5 in × 9,046 lbf = 904.6 lbf·in, about 75.38 lbf·ft, for a 1/2-13 Grade 5 bolt.
  • Metric equipment. A technician estimates an M12 class 8.8 bolt at about 88 N·m to reach 75% of its 48,874 N proof load.
  • Lubricant effects. An engineer sees that dropping K from 0.2 to 0.15 cuts the torque for the same 9,046 lbf preload by 25%.
  • Fixture building. A toolmaker targets 10,000 lbf of clamp on a 1/2 in bolt and estimates 1,000 lbf·in of torque with K = 0.2.
  • Engineering class. Students compare a Grade 5 and a Grade 8 1/2-13 bolt and find the Grade 8 can take 120 ÷ 85, about 1.41 times the torque.

Grade level and standards: Grades 6–7; Common Core State Standards for Mathematics 6.EE.A.2.c, 7.RP.A.3. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose inch or metric threads and pick the bolt size, or enter a custom diameter and pitch (thread spacing).
  2. Choose how to set the clamp load: a percentage of proof load (pick the grade or property class) or a load you enter.
  3. Pick the nut factor K that matches the thread condition, or enter one from the fastener or lubricant maker.
  4. Choose the torque unit. Then read the estimated torque, the preload it should produce, and the working behind it.

What the inputs mean

Bolt grade
SAE J429 grades are marked by lines on the bolt head, running out from the center: none for Grade 2, three for Grade 5 and six for Grade 8. Proof strengths are the standard's minimums for each size range.
Property class
ISO 898-1 property classes are stamped on the head, such as 8.8 or 10.9. Class 8.8 has a 580 MPa proof stress up to M16 and 600 MPa above.
Target preload
Proof load is the tension a bolt must carry without stretching for good. Tightening to 75% of it is a widely used starting target for joints that may be taken apart again. Permanent joints and gaskets often use other targets, set by the designer.
Nut factor (K)
K isn't a friction coefficient; it's a combined factor. NASA's Fastener Design Manual notes that 0.2 is the value commonly assumed for steel. But it says not to use that blindly, and that about 0.15 is more realistic for typical steel on steel. Its table gives K from about 0.07 with very slippery surfaces to 0.25 with friction coefficients of 0.2. Oil, anti-seize, thread lockers and platings all change K. So the same torque can give very different clamp loads.

Formula and method

T = K × D × F
tensile stress area (inch) = (π/4) × (D − 0.9743 ÷ TPI)²
tensile stress area (metric) = (π/4) × (D − 0.9382 × P)²
proof load = proof strength × tensile stress area
clamp load F = target % × proof load

D is the nominal (major, outside) diameter, and F is the bolt tension. TPI is threads per inch, and P is the metric pitch, the distance between threads in millimeters. π is pi, the circle constant. In inch units, T comes out in lbf·in (pound-force inches). With millimeters and newtons, it comes out in N·mm, which is divided by 1,000 for N·m. K has no units.

A threaded bolt is weakest through its threads. So its strength is based on the tensile stress area, an effective area a little larger than the area at the bottom of the threads. The constants 0.9743 and 0.9382 come from the inch and metric thread standards.

Worked example

A 1/2-13 UNC Grade 5 bolt is to be tightened to 75% of its proof load, dry, with K = 0.2.

  1. Stress area: (π/4) × (0.5 − 0.9743 ÷ 13)² = 0.1419 in².
  2. Proof load: 85,000 psi × 0.1419 in² = 12,061 lbf.
  3. Clamp load: 75% × 12,061 = 9,046 lbf.
  4. Torque: 0.2 × 0.5 in × 9,046 lbf = 904.6 lbf·in, which is 75.38 lbf·ft.

Result: About 75.38 lbf·ft should give roughly 9,046 lbf of clamp load. But with real-world friction, the actual preload could easily be 25% higher or lower.

Understanding the result

Treat the result as an estimate. It's the torque that gives the target preload under the friction you assumed. Say the threads are oiled but you used the dry K. Then the same torque stretches the bolt much harder and can yield it, stretching it for good.

Torque is an imprecise way to control tension. NASA's manual reproduces an industry table rating a torque wrench at about ±25% accuracy in preload. Tighter control needs other methods: turn-of-nut, load-indicating washers or measuring how much the bolt stretches.

Assumptions and limitations

  • A steel bolt and nut with standard 60° threads, tightened by turning the nut or head against a flat, hard washer face.
  • K stays the same and is known. Proof strengths are the standards' minimum values for each grade and size range.
  • Never use this in place of a manufacturer's torque specification. Head bolts, wheel lugs, connecting rods, suspension and brake fasteners, torque-to-yield bolts and structural connections have their own values and tightening orders.
  • It ignores the extra torque that locking nuts need (prevailing torque), from nylon inserts or deformed threads. You must add that on top.
  • It doesn't design the joint. Outside loads, fatigue, gasket crush, threads stripping in soft materials and parts settling (embedment relaxation) all need an engineer's analysis.

Frequently asked questions

What is the nut factor K?

It's a factor, based on tests, that links torque to tension. It covers thread friction, friction under the head and the shape of the threads. About 0.2 is commonly assumed for dry steel. Lubricated threads can be 0.15 or lower.

Why does lubrication matter so much?

Most of the torque you apply goes into overcoming friction in the threads and under the head. Lower friction lets more of the torque stretch the bolt. So a lubricated bolt tightened to a dry torque value can be badly overloaded.

Can I use this for wheel lug nuts or cylinder head bolts?

No. Use the vehicle maker's published torque and sequence. Many modern head bolts are torque-to-yield. They're tightened by angle after a first torque, which this formula doesn't model.

What torque does a metric M12 class 8.8 bolt need?

With K = 0.2 and 75% of the 580 MPa proof stress, the estimate is about 88 N·m. The bolt's or equipment's own specification comes first.

Sources

How this calculator is checked

Method: Short-form torque-tension relation T = K·D·F (NASA RP-1228); tensile stress area (π/4)(D − 0.9743/n)² for inch threads and (π/4)(D − 0.9382P)² for metric; proof strengths from SAE J429 and ISO 898-1 as summarized by the cited sources. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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