Calculate tensile stress or ultimate tensile strength from force and cross-section area in MPa, psi or ksi, or find the force or area for a given stress.
- All Construction Calculators
- Yield Strength Calculator
- Bolt Area Calculator (Thread Tensile Stress Area)
- Bending Stress Calculator
- Factor of Safety Calculator
- Punching Force Calculator
- Compressive Strength Calculator
Tensile Strength Formula
The following formula gives ultimate tensile strength when F is the peak force recorded in the tensile test and A is the original area. With an arbitrary applied force, F/A gives engineering tensile stress.
- Where TS is the tensile strength (Pa or psi)
- F is the peak force recorded during the tensile test (N or lbf), which can differ from the final fracture force
- A is the original cross-sectional area of the specimen (mยฒ or inยฒ)
This formula uses the original cross-sectional area of the test specimen, not the reduced area at the point of fracture. That distinction is important: using the original area gives what engineers call “engineering stress,” while using the instantaneous area at each moment of deformation gives “true stress.” Engineering stress is the standard reported value because it corresponds to the dimensions a designer actually specifies.
The calculator has stress, force, and required-area modes. In stress mode, the primary result is F/A and the optional secondary is stress/n. In force mode, the primary result is stress ร area and the optional secondary is force/n. Required-area mode uses A = F ร n / stress, with n = 1 when omitted; its equivalent solid-round diameter is d = โ(4A/pi). An entered factor below 1 is rejected. These arithmetic margins do not establish a code allowable or certified safe working load.
What Is Tensile Strength
Ultimate tensile strength (UTS) is the peak engineering stress recorded in the relevant tensile test: peak force divided by original cross-sectional area. It characterizes the tested material and conditions. The load capacity of an actual member also depends on geometry, connections, other failure modes, and applicable design provisions.
In a typical ductile-metal tensile test, force increases through elastic and plastic deformation to a peak, then may fall as localized necking develops before fracture. UTS is the peak force divided by original area. Other material classes can have different curve shapes; some brittle specimens fracture near their peak load with little visible necking.
Yield Strength vs. Ultimate Tensile Strength vs. Breaking Strength
These three values each describe a different point on the stress-strain curve and serve different roles in engineering design:
Yield strength is the stress at which a material begins to deform permanently. Below this value, the material returns to its original shape when the load is removed. For steels this is often identified by a distinct “yield point” on the curve. For aluminum and many other non-ferrous alloys, there is no sharp yield point, so engineers use a 0.2% offset method, drawing a line parallel to the elastic region offset by 0.2% strain and reading where it intersects the curve.
Ultimate tensile strength (UTS) is the peak of the engineering stress-strain curve, based on the original area. In common ductile-metal tests this peak is associated with the onset of localized necking. Design provisions can require separate yield- and rupture-based limit states rather than one universal strength divided by a chosen factor.
Breaking (fracture) strength refers to stress at specimen separation. Fracture engineering stress can be lower than UTS when the final fracture force is below the earlier peak force. Engineering stress retains the original-area denominator; a true fracture stress uses a different, instantaneous area measure. The relationship depends on material and test conditions.
Tensile Strength of Common Engineering Materials
The table below lists typical ultimate tensile strength values for widely used engineering materials. These are representative values; actual strength depends on alloy grade, temper, heat treatment, and manufacturing process. The “Specific Strength” column (UTS divided by density) shows how efficiently a material carries tensile load relative to its weight, which is a critical factor in aerospace and automotive lightweighting.
| Material | UTS (MPa) | UTS (ksi) | Density (g/cm3) | Specific Strength (kN-m/kg) |
|---|---|---|---|---|
| Low-carbon steel (AISI 1018) | 440 | 64 | 7.87 | 56 |
| Medium-carbon steel (AISI 1045) | 585 | 85 | 7.87 | 74 |
| Stainless steel 304 | 515 | 75 | 8.00 | 64 |
| Stainless steel 17-4 PH (H900) | 1310 | 190 | 7.78 | 168 |
| Tool steel (AISI D2) | 1850 | 268 | 7.70 | 240 |
| Aluminum 6061-T6 | 310 | 45 | 2.70 | 115 |
| Aluminum 7075-T6 | 572 | 83 | 2.81 | 204 |
| Titanium Ti-6Al-4V | 950 | 138 | 4.43 | 214 |
| Copper C11000 (pure) | 220 | 32 | 8.96 | 25 |
| Brass C36000 | 490 | 71 | 8.50 | 58 |
| Inconel 718 | 1240 | 180 | 8.19 | 151 |
| Gray cast iron (Class 40) | 293 | 42 | 7.15 | 41 |
| Nylon 6/6 | 85 | 12 | 1.14 | 75 |
| Polycarbonate | 65 | 9.4 | 1.20 | 54 |
| CFRP (unidirectional) | 1500 | 218 | 1.60 | 938 |
| E-Glass fiber (strand) | 3450 | 500 | 2.54 | 1358 |
| Kevlar 49 fiber | 3620 | 525 | 1.44 | 2514 |
| Spider silk (dragline) | 1000 | 145 | 1.30 | 769 |
Several patterns emerge from this data. Fiber materials dominate specific strength because they carry load almost entirely along their axis with very low density. Kevlar 49 fiber achieves a specific strength of roughly 2,514 kN-m/kg, about 45 times higher than that of low-carbon steel. Titanium Ti-6Al-4V and aluminum 7075-T6 both offer more than double the specific strength of mild steel, which explains their prevalence in aerospace structures where every kilogram of weight reduction translates to fuel savings over the life of an aircraft.
The Stress-Strain Curve and Where UTS Sits
A standard tensile test produces a stress-strain curve that reveals far more than just the UTS. Understanding the full shape of this curve is essential for anyone selecting materials or sizing structural members.
The curve begins with the elastic region, a straight line whose slope is the modulus of elasticity (Young’s modulus). In this zone, deformation is fully reversible. Steel has a Young’s modulus of about 200 GPa, aluminum about 69 GPa, and titanium about 114 GPa. A steeper slope means the material is stiffer and deflects less under the same stress.
At the yield point, the curve bends over and the material begins to deform plastically. Low-carbon steels often show an upper and lower yield point with a small load drop (the Luders band phenomenon), while most other alloys transition smoothly. The region between yield and UTS is the strain-hardening region. Here, dislocation density increases within the crystal lattice, making each successive increment of deformation require more stress.
In a common ductile-metal test, a force maximum can be followed by localized necking. Engineering stress then falls as force falls because its original-area denominator remains fixed. True stress uses instantaneous area and requires deformation information; its subsequent behavior cannot be inferred universally from the engineering curve alone. The specimen eventually separates at the fracture point.
The total area under the stress-strain curve up to fracture represents the material’s toughness, the total energy per unit volume the material can absorb before breaking. A material can have high UTS but low toughness if it fractures with very little strain (like a hard ceramic), or moderate UTS with high toughness if it stretches significantly before breaking (like annealed copper).
Factors That Affect Tensile Strength
Tensile strength is not a fixed property of a chemical composition alone. It is highly sensitive to processing history, environmental conditions, and microstructure. The major influencing factors include:
Temperature
Most metals lose tensile strength as temperature rises because thermal energy makes it easier for dislocations to move through the crystal lattice. Mild steel at 400 degrees C retains only about 60% to 70% of its room-temperature UTS. At cryogenic temperatures the opposite trend appears for many face-centered cubic (FCC) metals like austenitic stainless steels, which actually get stronger and remain ductile. Body-centered cubic (BCC) steels, however, become brittle at low temperatures, a phenomenon that contributed to the Liberty ship hull failures during World War II.
Grain Size
Smaller grains produce higher strength. Grain boundaries act as barriers to dislocation motion, so more boundaries mean more resistance to plastic deformation. This relationship is quantified by the Hall-Petch equation: yield stress increases proportionally to the inverse square root of the average grain diameter. A steel with a grain size of 10 micrometers will have a meaningfully higher yield and tensile strength than the same composition with a 100-micrometer grain size. Processes like thermomechanically controlled rolling and rapid cooling are used specifically to refine grain size in structural steels.
Strain Rate
Faster loading rates generally increase measured tensile strength. At quasi-static rates (around 0.001 per second, the standard testing speed), the material has time for dislocation rearrangement. At high strain rates (above 1,000 per second, as in impact or blast loading), there is insufficient time for thermal activation to assist dislocation motion, so the material resists deformation more strongly. This effect is more pronounced in BCC metals than FCC metals and is especially significant in polymers, where a factor of two increase in UTS between static and impact rates is common.
Heat Treatment and Cold Working
Heat treatment can dramatically change tensile strength without altering chemical composition. Quenching and tempering a medium-carbon steel like AISI 4140 can raise its UTS from about 655 MPa in the annealed condition to over 1,100 MPa. Precipitation hardening in alloys like aluminum 7075 or stainless steel 17-4 PH works by forming fine precipitates that block dislocation movement. Cold working (plastic deformation at room temperature) increases UTS through strain hardening but reduces ductility. A cold-drawn wire may have 30% to 50% higher UTS than the same alloy in the annealed state.
Defects and Surface Condition
Internal defects like porosity, inclusions, and micro-cracks act as stress concentrators that reduce effective tensile strength. Castings generally have lower UTS than wrought products of the same alloy because of trapped gas porosity and shrinkage voids. Surface scratches, machining marks, and corrosion pitting all create local stress concentrations that can initiate fracture well below the bulk UTS, especially under cyclic (fatigue) loading.
How Tensile Strength Is Measured
The standard test method for metallic materials in the United States is ASTM E8/E8M. A dog-bone-shaped specimen with a precisely machined gauge section is gripped in a universal testing machine and pulled at a controlled rate (typically 0.005 to 0.05 inches per minute for the yield region, then faster to fracture). The machine records force and displacement continuously, producing the raw data that becomes the stress-strain curve.
Key measurements taken from a standard tensile test include the 0.2% offset yield strength, the ultimate tensile strength, the percent elongation at fracture (measured over the original gauge length), and the percent reduction of area at the fracture cross-section. Elongation and reduction of area are ductility measures that complement the strength values. A typical structural steel like A36 shows about 20% elongation, while a high-strength spring steel might show only 5% to 8%.
For plastics, the equivalent standard is ASTM D638, and for composites ASTM D3039. Specimen geometry, grip design, and strain rate requirements differ between material classes because each behaves very differently under tension.
Tensile Strength in Engineering Design
Structural design uses the applicable code, material properties, service conditions, and relevant limit states. Design factors depend on the application and consequences of failure. A chosen numerical factor by itself does not account for yielding, fatigue, connections, instability, temperature effects, or material variability, and does not establish a universally safe design stress.
An AISC LRFD tension-member example checks gross-section yielding with 0.90 ร Fy ร Ag and rupture with 0.75 ร Fu ร Ae. The effective net area is Ae = U ร An, including the applicable shear-lag factor U, rather than assuming the bare net area always controls rupture resistance. These are LRFD resistance factors, not the calculatorโs chosen factor n; connection requirements and other applicable limit states must also be checked.
Pressure-vessel design must use the applicable ASME BPVC edition, construction section or division, permitted material and product form, temperature, and associated Section II, Part D stress tables and notes. Temperature-dependent and time-dependent properties may govern. A generic fraction of UTS or yield strength, or a user-selected factor alone, does not replace those requirements.
FAQ
Ultimate tensile strength (UTS) is the peak engineering stress recorded in the relevant tensile test: peak force divided by original cross-sectional area. An arbitrary applied force divided by original area gives engineering stress, and the final fracture force can differ from the peak. Values are reported in pressure units such as MPa or psi.
Yield strength identifies the onset of permanent deformation by the applicable test definition; UTS is the peak engineering stress in the tensile test. Their relationship depends on the material and conditions. Design provisions can require separate yielding and rupture checks with their applicable factors.
Among bulk engineering materials, ultra-high-strength steels (maraging steels) can reach UTS values above 2,400 MPa. Among fibers, carbon nanotubes have demonstrated tensile strengths above 60,000 MPa in laboratory conditions. For commonly available materials, Kevlar 49 fiber at 3,620 MPa and E-glass fiber at 3,450 MPa rank among the highest.
Yes. Most metals lose tensile strength at elevated temperatures because thermal energy assists dislocation movement. Mild steel at 400 degrees C retains only about 60% to 70% of its room-temperature UTS. However, some austenitic stainless steels actually increase in strength at cryogenic temperatures while remaining ductile.
ASTM E8/E8M is the standard test method for tensile testing of metallic materials. It specifies specimen geometry, strain rate, and reporting requirements. ASTM D638 covers plastics and ASTM D3039 covers fiber-reinforced composite materials.
