Calculate mechanical stress σ = F/A from a force and the cross-sectional area it acts on, solve for force or area instead, and read the result in Pa, kPa, MPa, or psi.
Enter the applied force and the cross-sectional area it acts over. Stress is force spread across area — the same force over a smaller area produces higher stress.
The signed load perpendicular to the cross-section, in newtons. Use positive for tension and negative for compression.
The area of the surface the force acts over, in square meters.
Default example: 1,000 N over 0.01 m² — a small steel bar in tension, giving σ = 0.1 MPa. This is nominal axial stress only; it does not check yield, buckling, fatigue, or local stress concentration.
Already know the stress? Solve for the force or the area instead of computing stress directly.
The applied load, in newtons.
The area the force acts over, in square meters.
The known or allowable stress, in megapascals.
Default example: solving for area at σ = 100 MPa and F = 5,000 N gives A = 50 mm².
A standalone stress-unit converter. Edit any one field and the other three update instantly — useful for translating a datasheet's psi rating into MPa, or vice versa.
Result
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Enter force and area to compute stress.
Pa—
kPa—
MPa—
psi—
4 min read4 steps6 terms3 examples6 FAQsσ = F / A
Mechanical stress describes how intensely a force is concentrated inside a material — the same force spread over a small area produces far higher stress than the same force spread over a large one.
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Walk-through
How to Use This Calculator
4 steps▸
1
Enter force and cross-sectional area
On the Stress tab, type in the applied force in newtons (N) and the cross-sectional area it acts over in square meters (m²). The calculator updates the stress instantly as you type.
2
Read the result in your preferred unit
The result card shows σ in megapascals (MPa) as the headline number, with pascals (Pa), kilopascals (kPa), and psi shown alongside it — no separate conversion step needed.
3
Or solve for force or area
Switch to the Solve tab if you already know the stress and one other value. Pick what you're solving for — Stress, Force, or Area — enter the other two, and the calculator rearranges σ = F/A for you.
4
Convert a standalone stress value
The Units tab is a free-standing converter: type a value into any of the Pa, kPa, MPa, or psi fields and the other three update automatically, independent of the Stress and Solve tabs.
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Reference
Formula & Methodology
2 formulas▸
Mechanical stress
σ = F / A
Stress (σ, the Greek letter sigma) is the internal force a material experiences per unit of cross-sectional area. F is the applied force in newtons (N), and A is the area that force acts over in square meters (m²). Because a newton per square meter is defined as a pascal, σ = F/A comes out directly in pascals (Pa) — no extra conversion constant is needed.
Rearranged for force or area
F = σA A = F / σ
The same relationship rearranges to solve for either of the other two variables: multiply stress by area to get force, or divide force by stress to get the required area. This is how engineers size a part — given a material's allowable stress and the load it must carry, solving for A gives the minimum cross-section needed.
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Glossary
Key Terms Explained
6 terms▸
Stress (σ) ↗The internal force per unit area that a material experiences under load. Measured in pascals (Pa) in SI units, or pounds per square inch (psi) in US customary units. Despite the everyday meaning of the word, mechanical stress is purely about force distributed over area — it has nothing to do with emotional strain.
Force (F) ↗The load applied to the material, measured in newtons (N). It can come from weight, tension in a cable, a clamping load, wind pressure integrated over a surface, or any other applied load.
Cross-sectional area (A) ↗The area of the surface the force acts perpendicular to — for a rod in tension, this is the area of the circular (or other) cross-section, not the rod's full surface area. Measured in square meters (m²).
Tensile stress ↗Stress that results from a force pulling a material apart, stretching it along the direction of the load. Cables, bolts under tension, and suspension-bridge hangers all carry tensile stress.
Compressive stress ↗Stress that results from a force pushing a material together, shortening it along the direction of the load. Columns, footings, and masonry piers typically carry compressive stress.
Pascal (Pa) ↗The SI unit of stress and pressure, equal to one newton per square meter (N/m²). Because a pascal is a small unit for structural loads, engineers usually work in kilopascals (kPa, ×1,000) or megapascals (MPa, ×1,000,000).
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Scenarios
Real-World Examples
3 worked examples▸
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Engineering student
A small steel bar in tension
Force, F 1,000 NCross-sectional area, A 0.01 m²
σ = 1,000 N ÷ 0.01 m² = 100,000 Pa = 0.1 MPa. That's a modest stress — mild steel typically yields around 250 MPa, so this bar has a lot of margin left before it deforms permanently.
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Mechanical designer
Sizing a bolt for an allowable stress
Solve for AreaForce, F 5,000 NAllowable stress, σ 100 MPa
A = F/σ = 5,000 N ÷ 100,000,000 Pa = 0.00005 m² = 50 mm². The bolt's cross-section needs to be at least 50 mm² to keep the stress at or below the 100 MPa allowable — roughly an 8 mm diameter round bar.
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Materials researcher reading a datasheet
Converting a psi rating to MPa
Given rating 14.5 psiTab used Units converter
14.5 psi converts to roughly 0.1 MPa (100,000 Pa) — the same stress as the first example, just expressed in US customary units. The Units tab handles this conversion directly without needing the force and area that produced it.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
Mechanical stress describes how intensely a force is concentrated inside a material — the same force spread over a small area produces far higher stress than the same force spread over a large one. It's the starting point for almost every structural and mechanical design calculation, from sizing a bolt to checking whether a beam will fail.
Why area matters as much as force
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A 1,000 N load sounds like a fixed quantity, but its effect on a material depends entirely on how much area it's spread across. Concentrate that same 1,000 N onto a needle-thin point and the stress is enormous — easily enough to pierce skin. Spread it across a 1 m² plate and the stress is trivial. This is why σ = F/A, not just F, is the number that predicts whether a material will yield, crack, or hold — force alone tells you nothing about the material's internal experience without knowing the area it's distributed over.
Tensile versus compressive stress
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The formula σ = F/A doesn't care which direction the force points, but the physical behavior does. A tensile force pulls a material apart — think of a cable holding a swing, or a bolt clamped in tension — and tends to stretch and eventually neck or fracture the material. A compressive force pushes the material together — a column supporting a roof, or a foundation footing — and tends to bulge, buckle, or crush it instead. Engineers usually track both types with sign conventions (tensile positive, compressive negative) since a material's strength limits often differ between the two.
From formula to real design decisions
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In practice, σ = F/A is rarely used just to compute a number in isolation — it's compared against a material's known strength limits (yield strength, ultimate strength, or a code-specified allowable stress) to check whether a design is safe. Rearranging the formula to A = F/σ is exactly how a designer sizes a part: given the load it must carry and the material's allowable stress, the minimum cross-sectional area falls straight out of the equation, often with a safety factor applied on top.
Limits of this simple model
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This calculator assumes the force is applied uniformly and perpendicular to a flat cross-section — a reasonable approximation for a straight rod, cable, or column under axial load. Real components often see combined loading (bending plus tension, for example), stress concentrations around holes and fillets, or shear forces acting parallel to the surface rather than perpendicular to it — see the companion Shear Stress Calculator for that case. For anything beyond simple axial loading, a full structural analysis or finite-element model is the appropriate next step, not this formula alone.
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Questions
Frequently Asked Questions
6 questions▸
What is the formula for stress?+
σ = F/A — stress equals the applied force divided by the cross-sectional area it acts over. Force is in newtons (N) and area is in square meters (m²), which gives stress directly in pascals (Pa) since a newton per square meter is defined as one pascal.
What units does this calculator use?+
Force is entered in newtons (N) and area in square meters (m²) on the Stress and Solve tabs. The result is shown in pascals (Pa), kilopascals (kPa), megapascals (MPa), and psi simultaneously. The Units tab lets you convert freely between all four without entering a force or area.
What's the difference between tensile and compressive stress?+
Both use the same σ = F/A formula — the difference is direction. Tensile stress comes from a force pulling the material apart (stretching it); compressive stress comes from a force pushing it together (squeezing it). The calculator computes the magnitude either way; whether it's tensile or compressive depends on which way your force is actually applied.
Is stress the same thing as pressure?+
They share the same units (pascals) and the same basic formula (force over area), but the terms are used in different contexts. Pressure usually describes a force from a fluid or gas acting on a surface; stress usually describes the internal force distribution within a solid material under load. Mathematically, for a simple uniform load, they're computed the same way.
Can I solve for force or area instead of stress?+
Yes — use the Solve tab and choose what you're solving for. Pick Force to compute F = σA from a known stress and area, or pick Area to compute A = F/σ from a known force and allowable stress. This is the common workflow for sizing a part to a target stress limit.
How does this relate to shear stress?+
This calculator covers normal stress, where the force acts perpendicular to the cross-section (pulling or pushing straight through it). Shear stress instead comes from a force acting parallel to the surface, sliding one layer past another — see the Shear Stress Calculator for that case, which uses the same τ = F/A form but with a different force direction.
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