How tight should the bolt be?

What the torque does

A bolt holds two parts together by being stretched like a stiff spring: the stretch pulls the parts against each other with the clamp load (preload). Tightening is only a way to get that stretch, and the wrench measures something else, the twisting force. Most of the torque never reaches the bolt: it is spent on friction under the head or nut and in the threads, and only the rest becomes tension. So the same torque can produce very different clamp loads depending on what the surfaces are like. The nut factor K lumps that friction into a single number, and this calculator uses it the way engineers do for quick estimates: T = K × d × F, torque equals K times the nominal diameter times the clamp load.

How the clamp load is chosen

The upper limit is the proof load, the load a bolt carries without staying stretched: the proof stress of its grade times the tensile stress area of the thread, π/4 × (D − 0.9743/n)² for inch threads with n threads per inch and π/4 × (d − 0.9382 × P)² for metric ones. A share of the proof load, 75 percent as a common default, is then used as the target. The proof stress is 55 ksi for SAE Grade 2 (up to 3/4 inch; 33 ksi above), 85 ksi for Grade 5 (up to 1 inch; 74 ksi above) and 120 ksi for Grade 8; and 580 MPa (600 MPa above M16) for class 8.8, 830 MPa for 10.9 and 970 MPa for 12.9.

Worked example

A 1/2-13 Grade 5 bolt has a stress area of 0.142 in², so its proof load is 85,000 psi × 0.142 in² = 12061 lbf. At 75 percent the clamp load is 9046 lbf, and with K = 0.20 the torque is 0.20 × 0.5 in × 9046 lbf = 905 lbf·in = 75.4 lbf·ft (102 N·m). An M12 × 1.75 class 8.8 bolt (stress area 84.3 mm², proof stress 580 MPa) has a proof load of 48.9 kN; 75 percent, 36.7 kN, takes 88 N·m at K = 0.20. The two tables show the results for other sizes, dry, at 75 percent: they are calculated here from the formulas above, not copied from a manufacturer's chart.

Limits of the method

The biggest uncertainty is K. NASA's manual shows K computed from the friction coefficients of the thread and the bearing surface, and the results span 0.074 to 0.25 for coefficients from 0.05 to 0.20, so friction alone can move the torque by a factor of three; a rusty, dirty, plated or lubricated bolt each has its own value. Next comes the tool: a torque wrench is good for about ±25 percent of clamp load in the figures NASA quotes. The method also assumes a new bolt tightened once; a reused bolt, a gasket that creeps, a soft or painted surface under the head, or a joint that is loaded by pressure or by vibration will not behave as the formula says. And the proof stresses here are the minimum of the grade for a plain steel bolt of the size listed; coated, stainless, aluminum or brass fasteners have other values.

How do I calculate bolt torque?

Use T = K × d × F: torque equals the nut factor K times the bolt diameter times the clamp load you want. Take the clamp load as a share of the bolt's proof load (proof stress times the thread's stress area), 75 percent being a common starting point. For a 1/2-13 Grade 5 bolt the proof load is 12061 pounds, 75 percent is 9046 pounds, and with K = 0.20 the torque is 0.20 × 0.5 in × 9046 lb = 905 lbf·in, or 75.4 lbf·ft.

What value of K should I use?

NASA's Fastener Design Manual (RP-1228) says the commonly assumed K = 0.2 should not be used blindly, and gives 0.15 as a more realistic typical value for steel on steel. K depends on the friction in the threads and under the head, so it falls with oil, wax or anti-seize and rises with rust, dirt and coarse finishes. Lubricant makers publish K for their products; if you have a number from a measurement, type it into the K field. The page can also compute K from friction coefficients with NASA's formula: for a fine-thread 1/2 inch bolt it gives 0.074, 0.133, 0.191, 0.250 for friction coefficients 0.05, 0.10, 0.15 and 0.20.

Should I use the dry or lubricated torque?

The one your table was made for, and no other. Oil or anti-seize lowers K, so the same wrench setting produces more clamp load. The dry figure for the Grade 5 1/2-13 bolt above, 75.4 lbf·ft, would give 100 percent of the proof load if the threads were oiled (K = 0.15 instead of 0.20): the bolt would be at its limit. With K = 0.15 the correct torque for 75 percent is 56.5 lbf·ft.

What do the grade markings mean?

SAE J429 grades for inch bolts are marked with radial lines on the head: no lines for Grade 2, three lines for Grade 5, six lines for Grade 8. Metric bolts show the property class: 8.8, 10.9 or 12.9, where the first number divided by 10 is the minimum tensile strength in 100 MPa units and the product of both numbers is the yield strength in 10 MPa units (class 8.8: 800 MPa tensile). The proof stress used here is 85 ksi (Grade 5, up to 1 inch), 120 ksi (Grade 8), 580 MPa (class 8.8 up to M16, 600 MPa above), 830 MPa (10.9) and 970 MPa (12.9).

How accurate is a torque wrench?

Less than most people think. NASA's manual quotes figures of the Industrial Fasteners Institute for the preload you get with each method: about ±35 percent by feel, ±25 percent with a torque wrench, ±15 percent by turn of the nut, ±10 percent with load-indicating washers and ±3 to 5 percent by measuring the elongation of the bolt. The scatter comes mostly from the friction, not the wrench, which is why the torque charts give a single number and a spread of 20 to 30 percent in the clamp load is normal.

Which torque is right for a wheel, an engine or a structure?

The one in the maker's or the engineer's specification. Wheel nuts, cylinder heads, connecting rods, pressure flanges and structural connections have a tightening procedure (a sequence, several passes, sometimes a final angle) and a specified lubricant, and the numbers in this calculator are neither. Use it for ordinary shop and household fastening and for checking a figure, not to replace a specification.

A starting point for ordinary shop and household fastening, not an engineering specification: critical joints (structure, pressure, wheels, engines, safety equipment) need the engineer's or manufacturer's torque and procedure. Sources: NASA Reference Publication 1228, R. T. Barrett, “Fastener Design Manual” (March 1990), “Alternative Torque Formula” and Tables VI and VII (T = KFd; K from friction; accuracy of torque-measuring methods, after the Industrial Fasteners Institute); SAE J429 proof loads (as tabulated by California Fastener) and ISO 898-1:2013 proof stresses (as tabulated by Universal Grip), because the standards themselves are not free; stress-area formulas from ISO 898-1 and ASME B1.1 as given by fastener references, which reproduce the tabulated M6 to M20 and 1/4 to 3/4 inch areas. Related: the physics torque calculator, tap drill calculator, hole pattern calculator and torque converter. How we check our calculators.