Axial Shortening & Compression Calculator
A free, browser-based calculator. Runs entirely in your browser — no sign up, nothing stored.
Enter Values
How to use this calculator
- Enter the axial load P (kN), the length in the direction of compression L (mm), the loaded area A (mm²) and the elastic modulus E (MPa).
- Optionally enter an allowable stress to get a quick stress check.
- Read the axial shortening, stress and strain.
How it works
Under a linear-elastic (Hooke's law) assumption, an axial load shortens a member by Δ = P·L ÷ (A·E). The stress is P ÷ A and the strain is stress ÷ E, so Δ = strain × L.
Compression and tension give the same magnitude — only the direction (shortening vs elongation) changes. The result is valid below the material's proportional limit.
Worked example
Slab: P = 2000 kN, L = 3000 mm, A = 200,000 mm², E = 30,000 MPa. Stress = 2,000,000 N ÷ 200,000 mm² = 10 MPa; strain = 10 ÷ 30,000 = 0.000333; shortening Δ = 0.000333 × 3000 = 1.000 mm.
Common mistakes
- Unit mismatch — keep P in kN, L in mm, A in mm² and E in MPa so Δ comes out in millimetres.
- Using a concrete short-term modulus where a long-term (creep-affected) value is needed, or vice versa.
- Forgetting that this is elastic only — it ignores creep, shrinkage, cracking and non-linear behaviour.
Frequently asked questions
What does PL/AE mean?
P is the axial load, L the length under compression, A the loaded cross-section area and E the elastic (Young's) modulus. Δ = P·L ÷ (A·E) is the elastic shortening.
What is elastic modulus E?
It's the stiffness of the material — stress divided by strain in the elastic range. Steel ≈ 200,000 MPa; concrete is roughly 25,000–35,000 MPa depending on strength and age.
Why does a larger area reduce shortening?
More area carries the same load at lower stress, so the strain (stress ÷ E) and therefore the shortening are smaller. Doubling the area halves the shortening.
Can I use it for tension?
Yes — the magnitude is the same; the member elongates instead of shortening, again within the elastic range.
Related tools
Tip: Enter any known values to calculate the remaining results.
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