What is the difference between stress and strain?

Stress is the internal force per unit area acting within a material when an external force is applied. It is measured in pascals (Pa) or newtons per square metre (N/m2). Strain is the resulting deformation expressed as a ratio: the change in length divided by the original length. Strain has no units because it is a dimensionless ratio. Stress causes strain; how much strain results from a given stress depends on the material's stiffness, characterised by Young's modulus.

How do you calculate Young's modulus?

Young's modulus (E) is calculated by dividing stress by strain: E = sigma / epsilon = (F / A) / (delta L / L0) = (F x L0) / (A x delta L). Here F is the applied force in newtons, A is the cross-sectional area in square metres, L0 is the original length in metres, and delta L is the extension (change in length) in metres. The result is in pascals (Pa). For most engineering materials, Young's modulus is expressed in gigapascals (GPa). Steel has a Young's modulus of approximately 200 GPa, aluminium about 69 GPa, and concrete about 30 GPa.

What is the elastic limit and why does it matter?

The elastic limit (also called the yield point) is the maximum stress a material can withstand and still return to its original shape when the load is removed. Below the elastic limit, stress and strain are proportional (Hooke's Law applies) and Young's modulus is constant. Above the elastic limit, the material deforms permanently (plastic deformation). This calculator assumes the material is within the elastic region. Engineers design structures so that working stresses stay well below the elastic limit, typically by applying a safety factor of 2 to 4 or more.

Stress and Strain (Young's Modulus) Calculator

Calculate tensile stress, tensile strain, and Young's modulus for any solid material. Enter the applied force, cross-sectional area, original length, and extension to get all three quantities instantly.

Formulae: Stress = F / A | Strain = δL / L₀ | Young's Modulus E = Stress / Strain

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Standard method Hooke's Law in the linear elastic region (ISO 6892-1, ASTM E111).

1. Applied Load

Applied force (F) tensile or compressive

Cross-sectional area (A) perpendicular to force

m²

Area unit helper converts to m²

2. Material Dimensions

Original length (L₀)

Extension / compression (δL)

Common material preset sets E for reference

Please enter positive numbers in all fields.

Results

Tensile Stress (σ)

F / A

Tensile Strain (ε)

δL / L₀ (dimensionless)

Young's Modulus (E)
-
σ / ε

Calculation Breakdown

Applied force (F)-

Cross-sectional area (A)-

Stress = F / A-

Original length (L₀)-

Extension (δL)-

Strain = δL / L₀-

Young's Modulus (E)-

Material Comparison

Your E value-

Closest common material-

Stress in MPa-

Strain as percentage-

Extension per metre-

Elastic region note-

Formulae used:

σ = F / A

ε = δL / L₀

E = σ / ε = (F × L₀) / (A × δL)

Result: Enter values above to see your result.

What Are Stress, Strain, and Young's Modulus?

When a force is applied to a solid object, two things happen simultaneously: the material develops an internal resistance (stress) and it changes shape (strain). Understanding these quantities is fundamental to mechanical and structural engineering, materials science, and physics.

Stress (sigma, σ) measures how much force acts on each square metre of cross-section inside the material. Strain (epsilon, ε) measures how much the material deforms relative to its original size. Young's modulus (E) is the ratio of stress to strain and is a fixed property of the material that describes its stiffness. A high Young's modulus means the material is stiff (like steel); a low value means it deforms easily under load (like rubber).

The Formulas

All three quantities are linked by simple relationships that hold in the elastic (linear) region:

Stress: σ = F / A, where F is the applied force in newtons (N) and A is the cross-sectional area perpendicular to the force in square metres (m²). Result is in pascals (Pa).
Strain: ε = δL / L₀, where δL is the change in length (extension or compression) in metres and L₀ is the original length in metres. Strain is dimensionless.
Young's modulus: E = σ / ε = (F × L₀) / (A × δL). Result is in pascals (Pa), typically expressed in gigapascals (GPa) for engineering materials.

These relationships hold only in the elastic region, below the yield (elastic limit) of the material. Beyond the yield point, the relationship becomes non-linear and permanent deformation occurs.

Worked Example

A steel rod has a cross-sectional area of 1 cm² (0.0001 m²) and an original length of 1 metre. A tensile force of 50,000 N is applied. The rod extends by 2.5 mm (0.0025 m).

Stress = 50,000 / 0.0001 = 500,000,000 Pa = 500 MPa
Strain = 0.0025 / 1 = 0.0025 (0.25%)
Young's Modulus = 500,000,000 / 0.0025 = 200,000,000,000 Pa = 200 GPa

This matches the accepted Young's modulus for structural steel (approximately 200 to 210 GPa), confirming the rod is within its elastic range.

Young's Modulus for Common Materials

Material	Young's Modulus (GPa)	Notes
Diamond	1,000	Stiffest known natural material
Steel (structural)	190 to 210	Standard value 200 GPa
Stainless steel	193 to 200	Similar to carbon steel
Titanium	116	High strength-to-weight ratio
Copper	110 to 128	Standard value 110 GPa
Brass	100 to 125	Varies by alloy
Aluminium alloy	68 to 72	Standard value 69 GPa
Glass (soda-lime)	65 to 72	Standard value 70 GPa
Concrete	25 to 35	Depends on mix and curing
Timber / Pine (parallel to grain)	9 to 14	Highly variable; moisture affects value
High-density polyethylene (HDPE)	0.7 to 1.4	Common engineering plastic
Rubber (natural)	0.01 to 0.1	Non-linear; this is the small-strain value

Units and Conversions

Stress and Young's modulus are measured in pascals (Pa). For practical engineering use:

1 MPa (megapascal) = 1,000,000 Pa = 1 N/mm²
1 GPa (gigapascal) = 1,000 MPa = 1,000,000,000 Pa
1 psi = 6,894.76 Pa; 1 ksi = 6.895 MPa

Cross-sectional areas: 1 cm² = 0.0001 m²; 1 mm² = 0.000001 m². Use the area unit helper in the calculator to avoid conversion errors.

Hooke's Law and the Elastic Region

These formulas apply only while the material obeys Hooke's Law, meaning stress and strain are proportional. In this linear elastic region, removing the load returns the material to its original dimensions. When stress exceeds the yield strength, the material enters the plastic region and permanent deformation occurs. Young's modulus is not valid beyond the yield point. Engineers typically design structural members so that working stress is no more than one-half to one-third of the yield strength, providing a safety factor.

Related Calculators

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Hooke's Law Spring Calculator: spring constant (k = F / x) for springs and elastic elements.
Force Calculator (F = ma): Newton's second law to find force, mass, or acceleration.
Hydraulic Cylinder Force Calculator: force from pressure and piston area in hydraulic systems.
Acceleration Calculator: find acceleration from velocity and time.

Method and sources: Formulae derived from Hooke's Law for elastic deformation: σ = F/A, ε = δL/L₀, E = σ/ε. Material Young's modulus values from Callister & Rethwisch, Materials Science and Engineering: An Introduction (10th ed.) and ASM International Material Property Data. ISO 6892-1:2019 (tensile testing of metallic materials). ASTM E111-17 (Young's modulus measurement).

This calculator is for educational and indicative engineering purposes only. Results assume isotropic, homogeneous material in the linear elastic region. Real materials may be anisotropic (such as timber or composites), and Young's modulus values vary with temperature, moisture content, manufacturing process, and alloy composition. Do not use these results as the sole basis for structural design. Consult a qualified structural or mechanical engineer for design work.