Example data table
These sample inputs show how diameter, load, and modulus influence strain. Replace them with your rope’s certified values for real work.
| Case | Diameter (mm) | Length (m) | Breaking load (kN) | Modulus (GPa) | Estimated strain (%) |
|---|---|---|---|---|---|
| A | 10 | 10 | 16 | 1.2 | 1.70 |
| B | 12 | 10 | 25 | 1.5 | 1.16 |
| C | 14 | 15 | 35 | 1.7 | 1.09 |
| D | 16 | 20 | 50 | 2.0 | 0.97 |
| E | 18 | 20 | 65 | 2.1 | 0.96 |
Formula used
- Strain: ε = ΔL / L0
- Percent strain: ε% = (ΔL / L0) × 100
- Area: A = π d² / 4
- Effective area: Aeff = A × k (k = fill/efficiency factor)
- Stress: σ = F / Aeff
- Strain: ε = σ / E
- Elongation: ΔL = ε × L0
Real ropes are nonlinear and construction‑dependent. Use certified test data for design, lifting, and safety‑critical work.
How to use this calculator
- Select a calculation method that matches your data.
- Enter rope diameter and an appropriate efficiency factor.
- Enter initial length, then either load or elongation at break.
- If using stress–modulus, provide Young’s modulus.
- Set a safety factor to estimate a working load limit.
- Press Calculate to view results above the form.
- Use the download buttons to export CSV or PDF.
Rope breaking strain guide
1) What “breaking strain” means
Breaking strain is the strain value at failure. Strain is dimensionless: ε = ΔL/L0. Many specifications report elongation at break as a percent, such as 5% or 12%, while test rigs report the corresponding breaking load. This calculator lets you work from either type of data.
2) Two practical input paths
If you know elongation at break, choose the elongation method and enter ΔL and L0. If you know breaking load and want an estimate of strain, choose the stress–modulus method. It converts load to stress using an effective area, then estimates strain with ε = σ/E.
3) Area, diameter, and why units matter
For a round rope, area scales with diameter squared: A = πd²/4. A small diameter change has a big effect. Example: increasing diameter from 12 mm to 14 mm raises area by about (14²/12²) = 1.36, roughly a 36% increase. Use consistent units; the tool converts mm, cm, in, and m.
4) Efficiency factor (k) and construction
Real ropes contain voids, fibers, strands, or wires that do not fully carry load as a solid rod would. The efficiency factor k adjusts the ideal area to an effective area: Aeff = A×k. Typical quick checks use k≈0.80–1.00. If you have test data, tune k so the estimate matches known results.
5) Typical modulus ranges to sanity‑check inputs
Young’s modulus varies widely by material and construction. As a rough guide: nylon ropes often fall near 0.5–1.0 GPa, polyester around 1–3 GPa, and steel wire ropes near 150–210 GPa. Use manufacturer datasheets when available; small E errors directly scale the strain estimate.
6) Stress, strain, and elongation outputs
The calculator reports strain in % or m/m and can also show breaking stress in Pa, kPa, MPa, GPa, or psi. When using stress–modulus, it also estimates elongation at break using ΔL = ε×L0, which helps compare with elongation‑based specifications and lab reports.
7) Safety factor and working load limit
Working load limit (WLL) is computed as WLL = Fbreak/SF. Common practice often uses SF values such as 5 for general lifting, 8–10 for more conservative lifting policies, and higher values for dynamic loading, shock, or life‑critical applications. Always follow local regulations and certified ratings.
8) A quick numeric example
Suppose d = 12 mm, k = 0.95, E = 1.5 GPa, and breaking load F = 25 kN. The effective area is Aeff ≈ 1.07×10⁻⁴ m², stress σ ≈ 234 MPa, and strain ε ≈ 0.156 (15.6%). If L0 = 10 m, elongation is about 1.56 m.
Use this article for estimation and cross‑checks. For engineering decisions, rely on certified rope tests, installation conditions, and safety standards.
FAQs
1) What is the difference between breaking load and breaking strain?
Breaking load is the force at failure. Breaking strain is the relative deformation at failure, ε = ΔL/L0. Two ropes can share the same breaking load but have different breaking strain due to material stiffness and construction.
2) Which method should I choose?
Use the elongation method when you know ΔL at break from testing or a datasheet. Use the stress–modulus method when you know breaking load and have an estimate of Young’s modulus to convert stress into strain.
3) Why is there an efficiency factor?
Ropes are not solid cylinders. Voids, braiding, strands, and core construction reduce the load‑carrying area. The efficiency factor scales the ideal area to a more realistic effective area for quick estimates.
4) Can I trust the estimated breaking stress?
It is a calculated average stress based on effective area. Real ropes have nonuniform stress distribution and nonlinear behavior. Treat the stress value as a comparison metric, not a certified material strength.
5) What safety factor should I use?
It depends on application, regulations, and inspection practices. Many lifting scenarios use 5, more conservative systems use 8–10, and dynamic or life‑critical systems can require higher. Follow manufacturer and legal guidance.
6) Why does diameter change results so much?
Area depends on d². A 10% diameter increase gives roughly a 21% area increase, lowering estimated stress and strain for the same load. Always measure diameter correctly and account for wear or flattening.
7) What if I only know percent elongation at break?
Convert percent elongation to strain by dividing by 100, or just use the elongation method: set ΔL = (percent/100)×L0. The calculator can display strain directly as a percent for convenience.