TIGERFASTENERS
Fastener calculators and formulas
Nineteen calculations that come up around screws and fasteners, from weight per thousand and thread dimensions to tightening torque and hardness conversion. Each section states the formula first, then gives a calculator that updates as you type. Every result is an estimate; acceptance and design follow the standard named on the drawing.
1. Weight per 1,000 pieces
m = V × ρ ÷ 1000
m is the mass of 1,000 pieces in kg, V the volume of one piece in mm³, and ρ the density in g/cm³. Since 1 mm³ × 1 g/cm³ = 0.001 g, the weight of one piece in grams is the weight of a thousand in kilograms. If you do not know the volume, estimate it with the next section.
This is a theoretical weight. Plating, chamfers, undercuts and dimensional tolerance all move the weighed figure away from it, so use it for quoting and material planning. Counting uses a weighed average piece weight instead, for the reasons in that box of 1,000 was weighed, not counted.
2. Estimating bolt volume in segments
V = Vhead + Vshank + Vthread
Split the bolt into head, plain shank and thread, work out each, and add them; then use the total in the section above. Hexagon head V = 0.866025 × S² × K; cylindrical head V = π/4 × dk² × k; shank V = π/4 × d² × Ls; thread V = π/4 × d₂² × Lt.
The thread uses the pitch diameter, not the stress diameter
The source manual computes the thread on the stress diameter ds = (d₂+d₃)/2. This calculator defaults to the pitch diameter d₂, for the reason the same manual gives in section 8: thread rolling is a constant-volume forming process and the blank is sized on d₂. Volume before rolling equals volume after, so the threaded length weighs what a d₂ cylinder weighs. Using ds understates the thread by 9% at M10 and 10% at M3. The manual's version is kept in the menu.
A countersunk head is a frustum, not a third of a cylinder
The manual takes a countersunk head as cylinder × 1/3, which is a full cone from a point. A 90° countersunk head is a frustum from the thread diameter d out to dk, with a short cylindrical rim on top. For ISO 7046-1 M3 (dk 5.5, k 1.65) the 1/3 rule gives 13.1 mm³ and the geometry gives 27.7 mm³, half as much again. Choosing countersunk here computes the geometry, with no factor.
Pan heads still use a factor. Modelling ISO 7045 M3 (dk 5.6, k 2.4) as a cylinder with its top edge rounded to k/2 gives 0.92; the manual's 0.75 would understate an M3×10 by about 9%. The default is 0.9. The same model gives 0.867 kg per 1,000 for M3×10, against 0.876 in a published ISO 7045 weight table.
Chamfers, washer faces, cross recesses and undercuts are not included. Where accuracy matters, weigh samples and correct the factor.
3. Theoretical weight of steel sections
m = A × L × ρ ÷ 1000
A is the cross-section in mm², L the length in metres, ρ the density in g/cm³; m comes out in kg. Copper and aluminium sections use the same formula with their own density.
| Wire dia. (mm) | kg/m |
|---|---|
| 5.5 | 0.187 |
| 6.5 | 0.260 |
| 8 | 0.395 |
| 10 | 0.617 |
| 12 | 0.888 |
| 14 | 1.208 |
| 16 | 1.578 |
| 20 | 2.466 |
| 25 | 3.853 |
Sections are made to tolerances, so this is an estimate. The angle ignores its root radius; for an exact figure use the standard section area for that size.
4. Volume of solids
Any consistent unit works: enter mm and get mm³, enter cm and get cm³.
5. Area of plane figures
Sector and segment use the exact geometric formulas. Angles are entered in degrees.
6. Basic thread dimensions and stress area
d₂ = d − 0.64952P d₃ = d − 1.22687P H = 0.866025P As = 0.7854 (d − 0.9382P)²
d₂ is the pitch diameter, d₃ the minor diameter of the external thread, and H the height of the fundamental 60° triangle. The stress area can also be written π/4 × [(d₂+d₃)/2]²; the two give the same result. As is used for tensile and proof load of external threads and does not depend on engagement length. Proof load Fp = Sp × As; minimum ultimate tensile load Fm = Rm × As.
Check: M10 × 1.5 gives As = 0.7854 × (10 − 0.9382 × 1.5)² = 58.0 mm²; at property class 10.9, Sp = 830 MPa and Fp = 830 × 58.0 = 48.1 kN.
Unified (UN) threads
As = 0.7854 (d − 0.9743 ÷ n)²
7. Blank diameter before thread rolling
dblank ≈ d₂ + Δ = (d − 0.64952P) + Δ
Thread rolling is constant-volume forming: material is pushed from the root up into the crest, so the blank is sized on the pitch diameter d₂, not on the major or minor diameter. The correction Δ depends on material, die condition and tolerance class, usually 0 to +0.04 mm.
Too small a blank leaves the crests unfilled and the pitch diameter undersize; too large overloads the dies, splits threads and raises burrs at the crest. ISO, DIN and JIS do not specify blank diameters; the right limits move with the thread tolerance class (6g, 6h and so on in ISO 965-1) and the material, so confirm them by trial rolling before production.
8. Thread engagement percentage and pilot hole
Dhole = D − 0.6495 × P × %
| Mating material | Lower | Upper |
|---|---|---|
| Steel | 55% | 85% |
| Aluminium | 65% | 100% |
| Cast iron | 60% | 80% |
| Plastic | 50% | 70% |
Higher engagement raises strip-out torque but also driving torque, which risks breaking or stripping the thread; for steel 70 to 75% is usual.
9. Tightening torque
T = K × d × F F = f × Sp × As
T is the torque, K the nut factor, d the nominal diameter and F the clamp load. Clamp load is usually 60 to 75% of the proof load (the preload factor f). With d in mm and F in kN, T comes out in N·m.
| Surface / treatment | K | Note |
|---|---|---|
| Plain, unlubricated (dry) | 0.20 | The usual default |
| Zinc electroplated (dry) | 0.22 | Higher friction |
| Zinc plated + lubricant / sealer | 0.18 | — |
| Zinc flake coating | 0.15 | Includes a lubricating layer |
| Phosphate + oil | 0.15 | — |
| Oiled / general lubrication | 0.15 | — |
| Molybdenum disulphide MoS₂ | 0.12 | Low friction |
| Stainless steel (dry) | 0.28 | Prone to galling; lubricate |
| Stainless steel + anti-seize | 0.18 | — |
Check: M10 × 1.5, class 10.9, K = 0.20, preload factor 0.70 gives As = 58.0 mm², Fp = 48.1 kN, F = 33.7 kN and T = 0.20 × 10 × 33.7 ≈ 67 N·m.
K depends on finish, lubrication, washers and the clamped material, and is the largest source of error in this formula, up to ±30%. For critical joints, confirm with a measured torque–tension curve or the turn-of-nut method.
10. Minimum breaking torque
MBmin = τB × WP τB = 0.6 × Rm WP = π d₃³ ÷ 12
τB is the torsional strength, usually taken as 0.6 × Rm, and WP the plastic torsional section modulus. The test is in ISO 898-7 (DIN EN 20898-7, JIS B 1058), which covers bolts and screws M1 to M10 of property classes 8.8 to 12.9, particularly below M3, where no tensile load is specified, and parts too short (L < 2.5d) for a tensile test. It does not apply to set screws.
Inch
Mb = d³ × UTS × 0.165
The two formulas are the same idea: 0.165 ≈ (π/12) × 0.63, the plastic section modulus times the torsion ratio. τB/Rm varies with material and heat treatment; before using it for acceptance, calibrate it against measured breaking torques.
11. Rivet length
Round head rivets
Steel L = 1.12Σδ + 1.4d Non-ferrous L = Σδ + 1.4d
Countersunk rivets
A = d₀² ÷ d² B = h(D² + D·d₀ − 2d₀²) ÷ 3d₀² L = A·Σδ + B + C
Round L up to the nearest standard length. C depends on the rivet diameter; take it from the standard you are using.
12. Clearance holes for bolts and screws
ISO 273 (DIN EN 20273, JIS B 1001) gives fine, medium and coarse series. Fine is for high precision and reliability (aerospace, automotive, marine), medium for general machinery and structures, and coarse for undemanding equipment.
| d | Fine | Medium | Coarse |
|---|---|---|---|
| M1.6 | 1.7 | 1.8 | 2 |
| M2 | 2.2 | 2.4 | 2.6 |
| M2.5 | 2.7 | 2.9 | 3.1 |
| M3 | 3.2 | 3.4 | 3.6 |
| M4 | 4.3 | 4.5 | 4.8 |
| M5 | 5.3 | 5.5 | 5.8 |
| M6 | 6.4 | 6.6 | 7 |
| M8 | 8.4 | 9 | 10 |
| M10 | 10.5 | 11 | 12 |
| M12 | 13 | 13.5 | 14.5 |
| M14 | 15 | 15.5 | 16.5 |
| M16 | 17 | 17.5 | 18.5 |
| M18 | 19 | 20 | 21 |
| M20 | 21 | 22 | 24 |
| M22 | 23 | 24 | 26 |
| M24 | 25 | 26 | 28 |
| M27 | 28 | 30 | 32 |
| M30 | 31 | 33 | 35 |
| M33 | 34 | 36 | 38 |
| M36 | 37 | 39 | 42 |
| M39 | 40 | 42 | 45 |
| M42 | 43 | 45 | 48 |
| M45 | 46 | 48 | 52 |
| M48 | 50 | 52 | 56 |
13. Hardness conversion (steel)
Enter a Vickers hardness; Brinell, Rockwell and tensile strength are interpolated linearly from the table below. Where a scale is not defined, the result shows a dash.
| HV | HB | HRC | HRB | Rm (MPa) |
|---|---|---|---|---|
| 80 | 76 | — | 41 | 255 |
| 100 | 95 | — | 56 | 320 |
| 120 | 114 | — | 67 | 385 |
| 140 | 133 | — | 76 | 450 |
| 160 | 152 | — | 84 | 515 |
| 180 | 171 | — | 89 | 575 |
| 200 | 190 | — | 93 | 640 |
| 220 | 209 | — | 96 | 705 |
| 240 | 228 | 20.3 | 100 | 770 |
| 260 | 247 | 24 | — | 835 |
| 280 | 266 | 27.1 | — | 900 |
| 300 | 285 | 29.8 | — | 965 |
| 320 | 304 | 32.2 | — | 1030 |
| 340 | 323 | 34.4 | — | 1095 |
| 360 | 342 | 36.6 | — | 1155 |
| 380 | 361 | 38.8 | — | 1220 |
| 400 | 380 | 40.8 | — | 1290 |
| 420 | 399 | 42.7 | — | 1350 |
| 440 | 418 | 44.5 | — | 1420 |
| 460 | 437 | 46.1 | — | 1485 |
| 480 | — | 47.7 | — | 1555 |
| 500 | — | 49.1 | — | 1595 |
| 520 | — | 50.5 | — | 1665 |
| 540 | — | 51.7 | — | 1740 |
| 560 | — | 53 | — | 1775 |
| 580 | — | 54.1 | — | 1845 |
| 600 | — | 55.2 | — | 1920 |
| 620 | — | 56.3 | — | 1995 |
| 640 | — | 57.3 | — | 2050 |
| 660 | — | 58.3 | — | 2115 |
| 680 | — | 59.3 | — | 2180 |
| 700 | — | 60.1 | — | 2240 |
| 720 | — | 61 | — | 2290 |
| 760 | — | 62.5 | — | 2400 |
| 800 | — | 64 | — | 2530 |
| 840 | — | 65.3 | — | — |
| 900 | — | 67 | — | — |
| 940 | — | 68 | — | — |
Valid only for unalloyed and low-alloy steel and cast steel, and approximate even there; stainless steel and non-ferrous metals convert differently. For acceptance, test with the method the drawing specifies.
14. Unit conversion
Length
Mass
Torque
Pressure / stress
Area
Volume
Temperature
15. Densities of common materials
| Material | ρ (g/cm³) | Note |
|---|---|---|
| Carbon / alloy steel | 7.85 | Common screw wire (SWRCH, 10B21, etc.) |
| Stainless steel 304 | 7.93 | Austenitic |
| Stainless steel 316 | 7.98 | Austenitic |
| Stainless steel 410 / 420 | 7.75 | Martensitic |
| Stainless steel 430 | 7.70 | Ferritic |
| Cast iron | 7.20 | — |
| Copper | 8.90 | — |
| Brass C36000 | 8.50 | — |
| Bronze | 8.80 | — |
| Aluminium / 6061 | 2.70 | — |
| Aluminium 7075 | 2.81 | — |
| Titanium TA2 | 4.51 | Equivalent to ASTM Grade 2 |
| Zinc | 7.14 | — |
| Magnesium alloy | 1.80 | — |
| Nylon PA66 | 1.14 | — |
| POM | 1.41 | — |
Use the value on the material certificate or specification where you have it.
16. Property classes
| Property class | Rm min (MPa) | Rp0.2 min (MPa) | Sp proof stress (MPa) | Material |
|---|---|---|---|---|
| 4.6 | 400 | 240 | 225 | Low-carbon steel |
| 4.8 | 420 | 340 | 310 | Low-carbon steel, cold-worked |
| 5.6 | 500 | 300 | 280 | Low-carbon steel |
| 5.8 | 520 | 420 | 380 | Low-carbon steel, cold-worked |
| 6.8 | 600 | 480 | 440 | Medium-carbon steel |
| 8.8 (≤ M16) | 800 | 640 | 580 | Medium-carbon steel, quenched and tempered |
| 8.8 (> M16) | 830 | 660 | 600 | Medium-carbon steel, quenched and tempered |
| 9.8 | 900 | 720 | 650 | Medium-carbon steel, quenched and tempered |
| 10.9 | 1040 | 940 | 830 | Alloy steel, quenched and tempered |
| 12.9 | 1220 | 1100 | 970 | Alloy steel, quenched and tempered |
| A2-70 / A4-70 | 700 | 450 | 450 | Austenitic stainless (ISO 3506) |
| A2-80 / A4-80 | 800 | 600 | 600 | Austenitic stainless (ISO 3506) |
Sp is used for the proof load Fp = Sp × As.
17. ISO metric thread basic dimensions
| Size | d | Coarse P | Fine P | d₂ | d₃ | As (mm²) |
|---|---|---|---|---|---|---|
| M1 | 1 | 0.25 | — | 0.838 | 0.693 | 0.46 |
| M1.2 | 1.2 | 0.25 | — | 1.038 | 0.893 | 0.73 |
| M1.4 | 1.4 | 0.3 | — | 1.205 | 1.032 | 0.98 |
| M1.6 | 1.6 | 0.35 | — | 1.373 | 1.171 | 1.27 |
| M2 | 2 | 0.4 | — | 1.740 | 1.509 | 2.07 |
| M2.5 | 2.5 | 0.45 | — | 2.208 | 1.948 | 3.39 |
| M3 | 3 | 0.5 | — | 2.675 | 2.387 | 5.03 |
| M3.5 | 3.5 | 0.6 | — | 3.110 | 2.764 | 6.78 |
| M4 | 4 | 0.7 | — | 3.545 | 3.141 | 8.78 |
| M5 | 5 | 0.8 | — | 4.480 | 4.019 | 14.18 |
| M6 | 6 | 1 | 0.75 | 5.350 | 4.773 | 20.12 |
| M8 | 8 | 1.25 | 1 | 7.188 | 6.466 | 36.61 |
| M10 | 10 | 1.5 | 1.25 | 9.026 | 8.160 | 57.99 |
| M12 | 12 | 1.75 | 1.25 | 10.863 | 9.853 | 84.27 |
| M14 | 14 | 2 | 1.5 | 12.701 | 11.546 | 115.44 |
| M16 | 16 | 2 | 1.5 | 14.701 | 13.546 | 156.67 |
| M18 | 18 | 2.5 | 1.5 | 16.376 | 14.933 | 192.47 |
| M20 | 20 | 2.5 | 1.5 | 18.376 | 16.933 | 244.79 |
| M22 | 22 | 2.5 | 1.5 | 20.376 | 18.933 | 303.40 |
| M24 | 24 | 3 | 2 | 22.051 | 20.319 | 352.50 |
| M27 | 27 | 3 | 2 | 25.051 | 23.319 | 459.41 |
| M30 | 30 | 3.5 | 2 | 27.727 | 25.706 | 560.59 |
| M33 | 33 | 3.5 | 2 | 30.727 | 28.706 | 693.55 |
| M36 | 36 | 4 | 3 | 33.402 | 31.093 | 816.72 |
| M39 | 39 | 4 | 3 | 36.402 | 34.093 | 975.75 |
| M42 | 42 | 4.5 | 3 | 39.077 | 36.479 | 1120.91 |
| M45 | 45 | 4.5 | 3 | 42.077 | 39.479 | 1306.01 |
| M48 | 48 | 5 | 3 | 44.752 | 41.866 | 1473.15 |
| M52 | 52 | 5 | 3 | 48.752 | 45.866 | 1757.84 |
| M56 | 56 | 5.5 | 4 | 52.428 | 49.252 | 2030.02 |
| M60 | 60 | 5.5 | 4 | 56.428 | 53.252 | 2362.02 |
| M64 | 64 | 6 | 4 | 60.103 | 56.639 | 2675.98 |
The fine-pitch column lists the common value only; a size can have several fine pitches, so follow the drawing.
18. Metric and inch thread comparison
| Size | Major (in) | Major (mm) | UNC TPI | UNF TPI | UNC pitch (mm) | Nearest metric |
|---|---|---|---|---|---|---|
| #0 | 0.0600 | 1.524 | — | 80 | — | M1.6 |
| #1 | 0.0730 | 1.854 | 64 | 72 | 0.397 | M2 |
| #2 | 0.0860 | 2.184 | 56 | 64 | 0.454 | M2 |
| #3 | 0.0990 | 2.515 | 48 | 56 | 0.529 | M2.5 |
| #4 | 0.1120 | 2.845 | 40 | 48 | 0.635 | M3 |
| #5 | 0.1250 | 3.175 | 40 | 44 | 0.635 | M3 |
| #6 | 0.1380 | 3.505 | 32 | 40 | 0.794 | M3.5 |
| #8 | 0.1640 | 4.166 | 32 | 36 | 0.794 | M4 |
| #10 | 0.1900 | 4.826 | 24 | 32 | 1.058 | M5 |
| #12 | 0.2160 | 5.486 | 24 | 28 | 1.058 | M5.5 |
| 1/4" | 0.2500 | 6.350 | 20 | 28 | 1.270 | M6 |
| 5/16" | 0.3125 | 7.938 | 18 | 24 | 1.411 | M8 |
| 3/8" | 0.3750 | 9.525 | 16 | 24 | 1.587 | M10 |
| 7/16" | 0.4375 | 11.112 | 14 | 20 | 1.814 | M11 |
| 1/2" | 0.5000 | 12.700 | 13 | 20 | 1.954 | M12 |
| 9/16" | 0.5625 | 14.287 | 12 | 18 | 2.117 | M14 |
| 5/8" | 0.6250 | 15.875 | 11 | 18 | 2.309 | M16 |
| 3/4" | 0.7500 | 19.050 | 10 | 16 | 2.540 | M20 |
| 7/8" | 0.8750 | 22.225 | 9 | 14 | 2.822 | M22 |
| 1" | 1.0000 | 25.400 | 8 | 12 | 3.175 | M24 |
| 1-1/8" | 1.1250 | 28.575 | 7 | 12 | 3.629 | M27 |
| 1-1/4" | 1.2500 | 31.750 | 7 | 12 | 3.629 | M30 |
| 1-3/8" | 1.3750 | 34.925 | 6 | 12 | 4.233 | M36 |
| 1-1/2" | 1.5000 | 38.100 | 6 | 12 | 4.233 | M39 |
| Size | TPI |
|---|---|
| 1/8" | 40 |
| 3/16" | 24 |
| 1/4" | 20 |
| 5/16" | 18 |
| 3/8" | 16 |
| 7/16" | 14 |
| 1/2" | 12 |
| 9/16" | 12 |
| 5/8" | 11 |
| 3/4" | 10 |
| 7/8" | 9 |
| 1" | 8 |
"Nearest metric" is a size comparison only. UN and metric threads have a 60° flank angle and BSW 55°; they are not interchangeable.
References
- ISO 261, ISO general purpose metric screw threads (DIN 13-1, JIS B 0205)
- ISO 273, clearance holes for bolts and screws (DIN EN 20273, JIS B 1001)
- ISO 898-1, mechanical properties of carbon and alloy steel bolts, screws and studs (DIN EN ISO 898-1, JIS B 1051)
- ISO 898-7, torsional test and minimum torques for bolts and screws, M1 to M10 (DIN EN 20898-7, JIS B 1058)
- ISO 3506-1, mechanical properties of stainless steel fasteners (DIN EN ISO 3506-1, JIS B 1054-1)
- ISO 7045, ISO 7046-1, cross-recessed pan and countersunk head screws (dimensions used for the pan factor and countersunk example; JIS B 1111)
- ISO 18265, hardness conversion for metallic materials (DIN EN ISO 18265); ASTM E140
- SAE J1701M, assembly torque for metric fasteners
Formulas and factors are compiled from the Wei Shiun Fasteners calculation handbook (20 September 2026). The two places this page departs from it, the thread diameter and the countersunk head volume, are explained in section 2.
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