Match the diagram conditions, then follow the example inputs and results. Change numerical values in the calculator.
1. Match the diagram to your question
ねじ面の斜面と座面を、別々の摩擦として扱う計算です。
有効径dm・リードℓ・ねじ山角と、ねじ面・座面それぞれの摩擦を用意します。
計算する方向
軸力から正作動トルク
軸方向の力 F
1,000 N
ねじの有効径 dm
10 mm
リード（ピッチ×条数）
1.5 mm
ねじ山の半角
30 °
ねじ面の摩擦係数
0.15
座面の摩擦係数
0.15
座面の等価摩擦直径
15 mm
この例は軸力Fから締付け方向のトルクTを求めます。逆方向や緩める条件とは分けます。
T · 正作動・締付け方向トルク
2.23897 N·m
計算する軸力
1,000 N
リード角
2.7336 °
The calculation treats thread and bearing-face friction separately.
Prepare pitch diameter dm, lead ℓ, thread angle and separate thread and bearing friction.
Calculation direction
Axial force → raising/tightening torque
Axial force F
1,000 N
Thread pitch diameter dm
10 mm
Lead (pitch × starts)
1.5 mm
Thread half angle
30 °
Thread friction coefficient
0.15
Bearing/collar friction coefficient
0.15
Equivalent bearing friction diameter
15 mm
This example converts axial force F to tightening torque T. Keep loosening and reverse conditions separate.
T · Raising / tightening torque
2.23897 N·m
Calculated axial force
1,000 N
Lead angle
2.7336 °
Blue marks inputs; orange marks outputs. These diagrams explain the fixed example below; dimensions and deformation are not drawn to physical scale.
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2. Example inputs
Calculation directionWhat goes here?
Choose the option matching your mechanism and diagram. A different model can change required inputs and applicable results.
Axial force → raising/tightening torque
Axial force FWhat goes here?
Magnitude of a push or pull, in force units such as N, rather than mass in kg.
1,000 N
Thread pitch diameter dmWhat goes here?
Use the dimension marked in the diagram. Distinguish radius from diameter, bore from outside diameter, and overall length from support span.
10 mm
Lead (pitch × starts)What goes here?
Use the dimension marked in the diagram. Distinguish radius from diameter, bore from outside diameter, and overall length from support span.
1.5 mm
Thread half angleWhat goes here?
Match the field symbol to the diagram and check dimensions, specifications or operating conditions. Replace example numbers with your actual conditions.
30 °
Thread friction coefficientWhat goes here?
Sliding friction at the thread flanks; it is different from the empirical nut factor K.
Lubrication, screw/nut pairing and coatings affect this value. The manufacturer notes it can exceed the reference range. Do not apply it universally to bolts or lead screws. Enter bearing-surface friction separately.
Choose values for actual contact, lubrication, temperature and other conditions. These initial values are examples.
Friction at the head/nut bearing surface, used with its effective diameter separately from thread friction.
These are hypothetical comparisons, not material recommendations. Match coating, lubrication, washers and reuse conditions. Do not enter a nut factor K as this μ.
Choose values for actual contact, lubrication, temperature and other conditions. These initial values are examples.
Use the dimension marked in the diagram. Distinguish radius from diameter, bore from outside diameter, and overall length from support span.
15 mm
These are fixed teaching inputs. Coefficients, properties and comparison limits are not recommendations. Enter your conditions in the calculator.
3. Results for this example
Raising / tightening torque
2.23897 N·m
Calculated axial force
1,000 N
Lead angle
2.7336 °
This example starts with 1,000 N axial force and finds tightening-direction torque. For inverse calculation, change direction while retaining matching dimensions and friction.
4. Which formula is used?
λ = atan(ℓ/(πdm)); μ′ = μ/cosα; cT = (dm/2)tan(λ+atanμ′)+μbDb/2; T = F cT; Tlower = F[(dm/2)tan(atanμ′−λ)+μbDb/2]
Table units are not always the units required in the formula. The calculator converts selected units to its internal base units before computing.
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Assumptions and exclusions
Quasi-static sliding thread friction. Lead differs from pitch on multistart screws. Separate from rolling-efficiency ball screws and empirical nut-factor preload. Specify actual effective bearing diameter and friction.
