Tensile Stress Calculator
Tensile stress is σ = F / A: a 10 kN load on a 10 mm diameter bar (A = 78.54 mm²) gives 127.3 MPa, or 18.47 ksi.
127.323954473516 MPa
Full answer, then cut to fewer decimals (not rounded):
- 127.323954473516 MPa
- 127.32395447351 MPa
- 127.3239544735 MPa
- 127.323954473 MPa
- 127.32395447 MPa
- 127.3239544 MPa
- 127.323954 MPa
- 127.32395 MPa
- 127.3239 MPa
- 127.323 MPa
- 127.32 MPa
- 127.3 MPa
- A = 78.5398 mm² = 0.0000785398 m²
- σ = 10000 N ÷ 0.0000785398 m² = 127324000 Pa
- = 18466.8 psi
- = 18.4668 ksi
- = 12.9834 kgf/mm²
Stress Formula and Cross-Sections
σ = F / A
σ normal stress (Pa = N/m²; N/mm² = MPa), F axial force (N), A cross-sectional area (m² or mm²)
| Section | Area A |
|---|---|
| Round bar or wire, diameter d | π d² / 4 |
| Rectangle or flat bar, b × h | b × h |
| Round tube, outside D, inside d | π (D² − d²) / 4 |
This is the average (engineering) stress over the original section. Holes, notches and threads raise the local stress; for bolts use the tensile stress area from the thread standard rather than the shank diameter.
Worked Examples
- 10 kN on a 10 mm round bar: A = π × 10² / 4 = 78.54 mm², σ = 10 000 ÷ 78.54 = 127.3 MPa.
- 100 kN on a 50 × 8 mm flat bar: A = 400 mm², σ = 250 MPa (36.26 ksi).
- 50 kN on a 60.3 × 3.9 mm tube: A = π (60.3² − 52.5²) / 4 = 691 mm², σ = 72.36 MPa.
- 10 000 lbf on a ½ in bar: A = 0.1963 in², σ = 50930 psi = 351.1 MPa.
Frequently asked questions
What is the formula for tensile stress?
Engineering stress is the axial force divided by the original cross-sectional area: σ = F / A. A force in newtons over an area in mm² gives N/mm², which is the same as MPa.
What is the difference between stress and strength?
Stress is what a load produces in a part; strength (yield or ultimate tensile strength) is the stress a material can withstand. A part is safe when the working stress stays below the yield strength divided by the safety factor.
How do I find yield stress from a tensile test?
Divide the force at yield (or at 0.2 % offset) by the original cross-sectional area of the specimen. Use the original area, not the necked area, for engineering stress.
Is N/mm² the same as MPa?
1 N/mm² = 1 MPa exactly, because 1 mm² = 10⁻⁶ m².
Does this work for compression?
Yes, σ = F/A gives the average compressive stress too. Slender members in compression can buckle at a much lower stress, which this formula does not check.
What is the SI unit and symbol of tensile stress?
Stress is written σ (sigma) and its SI unit is the pascal (Pa = N/m²). Engineers usually use MPa (= N/mm²); in US units it is psi or ksi.
What is the difference between tensile and compressive stress?
Both are σ = F/A. Tensile stress pulls the material apart (the bar gets longer); compressive stress pushes it together (the bar gets shorter). By convention tension is positive and compression negative.
What is the tensile stress area of a bolt?
Bolts are checked on the tensile stress area of the thread, not the shank: for ISO metric threads A_s = (π/4)(d − 0.9382 P)², with d the nominal diameter and P the pitch. An M10 × 1.5 bolt has A_s ≈ 58.0 mm² and an M12 × 1.75 bolt about 84.3 mm².
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 2008 Edition, National Institute of Standards and Technology .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Tensile Stress Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/tensile-stress/
IEEE
Scientific Converters, "Tensile Stress Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/tensile-stress/