Educational explanation, not professional design advice. Last reviewed 24 October 2026. Disclaimer
In plain English
Pull a bar harder and harder and it eventually stretches, thins in one place and snaps. The highest stress it reached on the way is its tensile strength — the most load per unit area the material can carry in tension. It is the headline “strength” figure on many material data sheets.
Technical definition
Tensile strength Rm (ultimate tensile strength, UTS) is the stress corresponding to the maximum force Fm in a tensile test, calculated on the original cross-sectional area (ISO 6892-1). Beyond this point a ductile metal starts to neck — the deformation concentrates in one region — and the force falls until fracture.
How it works and where it is used
The same tensile test that gives yield strength gives Rm. The test also reports elongation after fracture A (the permanent increase in gauge length) and often reduction of area, which show how ductile the material is. A high tensile strength with very low elongation indicates a hard, brittle material.
Formula
Rm = Fm ÷ S0 A = (Lu − L0) ÷ L0 × 100%
Fm = maximum force, S0 = original cross-sectional area, L0 = original gauge length, Lu = final gauge length after fracture.
Worked example
The illustrative specimen from the yield-strength article (Ø10.0 mm, S0 = 78.54 mm², gauge length 50 mm) reaches a maximum force of 33.0 kN and measures 63 mm between the gauge marks after fracture.
- Rm = 33 000 ÷ 78.54 = 420 MPa
- A = (63 − 50) ÷ 50 = 26% — a ductile material
- Yield-to-tensile ratio = 270 ÷ 420 = 0.64
In the workshop and in practice
Tensile strength is used to grade materials and fasteners (for example, the first number in a metric bolt property class relates to its nominal tensile strength), to estimate fatigue strength in early design, and in quality control of incoming material. For machining, stronger and harder materials generally need lower cutting speeds and more cutting force.
Common mistakes and misconceptions
- Designing to tensile strength for static loads. Most designs limit stress below yield, with a factor of safety.
- Equating strength with toughness. A very strong material can still crack easily if it is brittle.
- Using engineering stress after necking to describe the true stress in the neck — it is higher than the engineering value.
Related calculators
- Bolt Tightening Torque Estimator — Tightening torque from preload (T = K·F·d), preload from torque, or a preload target from proof strength.
- Shaft Torsional Stress Calculator — Torsional shear stress and angle of twist of a round shaft, or the diameter needed.
Related topics
- Yield Strength — The stress at which a material starts to deform permanently.
- Stress and Strain — Internal force per unit area, and the stretch per unit length it causes.
References
- ISO 6892-1: Metallic materials — Tensile testing — Part 1: Method of test at room temperature (Rm, elongation A)
- ASTM E8/E8M: Standard Test Methods for Tension Testing of Metallic Materials
- Callister and Rethwisch, Materials Science and Engineering: An Introduction