Screw Calculator

Pitch · Travel Distance · Torque · Force

Screw Calculator

Select calculation:

Calculate travel distance

Calculate pitch

Calculate rotations

Calculate torque

Calculate force

Pitch p [mm] M10: 1.5 mm | M16: 2 mm | M20: 2.5 mm

Rotations n [Count]

Formulas & Symbols

Key Formulas

Travel distance (axial displacement):
h = p × n
h = travel [mm], p = pitch [mm], n = rotations

Pitch:
p = h / n
Axial displacement per rotation

Torque (simplified):
M ≈ F × (p / (2π)) × (1 / η)
or with friction: M = F × d/2 × tan(α + ρ)

Friction angle:
ρ = arctan(μ)
μ = coefficient of friction

Flank angle:
α = 30° (ISO metric thread)
also: thread flank inclination angle

Symbol Reference

h	Travel distance / axial displacement [mm]
p	Pitch [mm]
n	Rotations [count]
M	Torque [N·m]
F	Axial force [N]
d	Thread diameter [mm]
α	Flank angle [°]
ρ	Friction angle [°]
μ	Coefficient of friction [0…1]

Screw – Fundamentals

What is a screw?

A screw is an inclined plane spiraled around a cylinder. It converts a rotary motion (rotations) into linear motion (travel, axial displacement) – and is one of the most effective ways to generate large axial forces. You find it everywhere: in clamping, fastening, presses, spindles, rack railways, and precision gauges.

The thread of a screw is defined by its pitch (mm per rotation). A finer pitch provides higher force multiplication with fewer rotations; a coarser pitch allows faster travel.

Advantages

Very high force multiplication
Self-locking (at low pitch)
Simple construction
High precision achievable
Wide selection of threads (ISO, UNC, etc.)
Cost-effective

Disadvantages

Slow travel (fine pitches)
Friction losses per rotation
Wear from friction
Regular maintenance required
Vibrations possible

Thread Types and ISO Sizes

Various thread types exist: Metric Thread (ISO, flank angle 30°), Whitworth, UNC/UNF (USA), Trapezoidal Thread (for spindles). The standard determines diameter, pitch, and allowed tolerances.

Common metric pitches (ISO 262):
M6: 1.0 mm | M8: 1.25 mm | M10: 1.5 mm | M12: 1.75 mm | M16: 2.0 mm | M20: 2.5 mm | M24: 3.0 mm

Detailed Formula Derivations

1. Travel Distance h

Travel is the axial displacement after n rotations:

h = p × n
Example: pitch p = 1.5 mm, n = 10 rotations → h = 1.5 × 10 = 15 mm

2. Pitch p

Pitch is the axial displacement per rotation:

p = h / n
Example: travel h = 15 mm, n = 10 rotations → p = 15 / 10 = 1.5 mm

3. Torque M (Screw Force Relationship)

The required torque to generate an axial force F depends on friction, pitch, and diameter. Simplified:

M ≈ F × (p / (2π)) × (1 / η)
η = efficiency (typically 0.5–0.9)

More precisely (with friction angle ρ = arctan(μ) and flank angle α = 30°):

M = F × (d/2) × tan(α + ρ)
This accounts fully for screw geometry and friction effects.

4. Force from Torque

Reverse calculation:

F = M / ((d/2) × tan(α + ρ))
Calculate axial force from applied torque

Practical Load Calculation

Thread Size	Pitch	Typical Load
M6	1.0 mm	2–5 kN
M10	1.5 mm	10–20 kN
M16	2.0 mm	30–50 kN
M20	2.5 mm	50–100 kN
M24	3.0 mm	80–150 kN

Rule: Self-Locking

Self-locks when: ρ > α/2
Metric (α = 30°): μ > tan(15°) ≈ 0.27
With lubrication (μ ≈ 0.10): not self-locking
Dry friction: self-locking

Worked Example – M16 Fastening

Given:
M16 screw (diameter d = 16 mm, pitch p = 2 mm)
Required axial force F = 50,000 N (50 kN)
Coefficient of friction μ = 0.15 (lubricated steel)
Flank angle α = 30° (ISO metric)

Step 1: Friction Angle

ρ = arctan(0.15) ≈ 8.53°

Step 2: Required Torque

M = F × (d/2) × tan(α + ρ)
M = 50,000 × (16/2) × tan(30° + 8.53°)
M = 50,000 × 8 × tan(38.53°)
M ≈ 50,000 × 8 × 0.785 ≈ 314 N·m

Step 3: Required Rotations (Example: 10 mm travel)

n = h / p = 10 / 2 = 5 rotations

Result: To clamp an M16 screw at 50 kN, approximately 314 N·m torque and 5 rotations are required. This is typical for high-load fastening in mechanical engineering and construction.

Applications

Clamping Technology

Bench vise
Clamp jaws
Clamping chuck
C-clamps / Vises

Machine Tools

Fastening connections
Lead screw / spindle
Worm gear drive
Rack railway

Precision Measurement

Micrometer screw
Precision measurement tools
Adjustment threads
Positioning pins

Frequently Asked Questions

Self-locking occurs when the friction angle ρ is greater than half the flank angle α. This means the screw won't back out on its own (even under load) – friction holds the load. For metric threads: self-locking when μ > tan(15°) ≈ 0.27. This is typical for dry friction, but not with lubrication.

Pitch (p) is the axial displacement per rotation [mm]. Flank angle (α) is the geometric angle of the thread flank (e.g., 30° for ISO metric). Pitch is given in mm; flank angle in degrees.

Pitch is standardized per ISO 262. Larger diameters typically get coarser pitches – this optimizes the balance between load capacity and working speed. M6 has 1.0 mm, M16 has 2.0 mm, M24 has 3.0 mm.

Lubrication reduces friction, which significantly lowers required torque – typically 20–50 %. Coefficient of friction drops from 0.20–0.25 (dry) to 0.10–0.15 (lubricated). This is critical for high-torque applications (e.g., motors, presses).

Fine pitch (e.g., M16 × 1.5) has smaller pitch than coarse pitch (M16 × 2). Fine pitch: higher force multiplication, self-locking, fine adjustment. Coarse pitch: faster, less torque needed. Choice depends on application.

Summary

Screw converts rotary to linear motion and generates large axial forces.
Travel h = p × n: displacement from pitch and rotations.
Torque M = F × (d/2) × tan(α + ρ): depends on force, diameter, friction.
Pitch per ISO 262: M6: 1.0 | M10: 1.5 | M16: 2.0 | M20: 2.5 mm
Flank angle (metric): α = 30°.
Self-locking when μ > tan(15°) ≈ 0.27 (dry friction).
Lubrication reduces torque by 20–50 %.
Applications: fastening, clamping, spindles, precision measurement.

Ist diese Seite hilfreich?

Vielen Dank für Ihr Feedback!

Das tut uns leid
Wie können wir die Seite verbessern?

Screw Calculator