There are two ways to answer “what’s the tensile strength” depending on what you already have. If you already know the maximum force a part carried before failing and its original cross-sectional area, it’s a one-line calculation: σ = F_max / A₀. If you don’t have those numbers yet, you need to run an actual tensile test — pull a standardized specimen apart on a testing machine until it breaks, and record the numbers the calculation needs. This article covers both: the formula for when you have the data, and the full test procedure for when you don’t.
If You Already Have the Force and Area: The Formula
Tensile Strength (σ) = F_max ÷ A₀
Where:
- F_max = the maximum force the specimen carried before fracture (N or lbf)
- A₀ = the original cross-sectional area of the specimen, measured before loading (mm² or in²) — not the narrower area at the point of fracture
For a round specimen: A₀ = π × d² / 4 (where d is the original diameter) For a rectangular specimen: A₀ = width × thickness
Worked Example
A steel rod with a 10 mm diameter is pulled to failure at a maximum load of 31.4 kN (31,400 N):
- Calculate the original area: A₀ = π × (10)² / 4 = 78.54 mm²
- Divide: σ = 31,400 N ÷ 78.54 mm² ≈ 400 MPa
Since 1 N/mm² = 1 MPa, no unit conversion is needed when working in millimeters and newtons. This same formula applies whether the number you’re after is called “tensile strength” or “ultimate tensile strength (UTS)” — the two terms describe the same calculation on the same peak-force data point. See What Is Tensile Strength? if you need the conceptual distinction between yield strength, UTS, and fracture strength — that’s a definitional question, not a calculation difference.
If You Don’t Have the Data Yet: How to Run the Test
Tensile strength testing is a destructive mechanical test: a standardized specimen is pulled apart until it breaks, and the machine records force and elongation throughout to build the numbers the formula above needs — plus several other material properties along the way.
- Prepare the specimen. Machine or cut the material into a standardized shape — commonly a “dog-bone” shape for metals and plastics, with a narrower gauge section so failure occurs away from the grips rather than at the clamped ends. For metals, ASTM E8/E8M is the standard reference for specimen dimensions and test procedure; the exact geometry depends on material and thickness.
- Measure the original cross-section. Record the gauge section’s width/thickness or diameter before any load is applied — this becomes A₀ in the formula.
- Mount the specimen. Clamp both ends into the grips of a Universal Testing Machine (UTM), aligned axially so the load pulls straight along the specimen — misalignment introduces bending stress that skews the result. An extensometer is often attached to the gauge section to track elongation precisely.
- Apply tension at a controlled rate. The machine pulls the specimen apart at a constant speed (or controlled strain rate), continuously recording applied force and elongation.
- Continue to fracture. The specimen passes through elastic deformation, then yields and deforms plastically, typically necks down in cross-section, and finally fractures. The highest force recorded during the entire test is F_max.
- Calculate tensile strength. Divide F_max by the original area A₀ (step 2) — this is the formula from the section above.
The test produces a full stress-strain curve, not just the tensile strength number. From the same test run, you also get:
| Property | What it tells you |
|---|---|
| Yield strength | Stress at which the material stops behaving elastically and begins permanent deformation |
| Ultimate tensile strength (UTS) | Maximum stress before fracture — this is “tensile strength” in the everyday sense |
| Elongation / ductility | How much the specimen stretched before breaking — brittle vs. ductile behavior |
| Young’s modulus | Stiffness — the slope of the elastic (initial, straight-line) portion of the curve |
| Reduction of area | How much the cross-section narrowed at the fracture point |
Which Approach Do You Actually Need?
- You have force and dimensions from a test report or a known spec → use the formula directly. This is the fast path if someone hands you F_max and A₀.
- You’re evaluating an actual physical part or material sample and don’t have prior test data → you need the full test procedure — there’s no shortcut to generating F_max without pulling the material to failure on a UTM.
- You’re trying to find a published number for a known material/grade (e.g., “what’s the tensile strength of A36 steel”) → neither of the above — see What Is the Tensile Strength of Steel? for a per-grade reference table instead of re-deriving it from scratch.
Related reading: What Is Tensile Strength? · What Is the Tensile Strength of Steel?
