Library / Tools / A-level physics equation calculator / Young modulus

Young modulus calculator

A-level Materials

The Young modulus is the stress divided by the strain in the region where a material obeys Hooke’s law.

E = σ / ε

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

EYoung modulus to find 2.00 × 10¹¹ Pa

σStress

εStrain

Significant figures

Working

Write the equation
E = σ / ε
Substitute the values
E = (1.2 × 10⁸) ÷ (6 × 10⁻⁴)
Calculate
E = 2 × 10¹¹ Pa
Give the answer to 3 significant figures
E = 2.00 × 10¹¹ Pa

Worked example

Find E, the Young modulus. Given: stress σ = 1.20 × 10⁸ Pa; strain ε = 6.00 × 10⁻⁴.

Write the equation
E = σ / ε
Substitute the values
E = (1.2 × 10⁸) ÷ (6 × 10⁻⁴)
Calculate
E = 2 × 10¹¹ Pa
Give the answer to 3 significant figures
E = 2.00 × 10¹¹ Pa

Symbols and units

Symbol	Quantity	SI unit
E	Young modulus	Pa
σ	Stress	Pa
ε	Strain	no unit

Young modulus: rearranged

To find Young modulus: E = σ / ε
To find stress: σ = E ε
To find strain: ε = σ / E

Exam tip

Typical values are about 200 GPa for steel. The unit selector can give the answer in GPa.

Common questions

What is the formula for young modulus?

The equation is E = σ / ε, where E is the Young modulus (Pa); σ is the stress (Pa); ε is the strain.

What units should I use for young modulus?

In SI units: Young modulus in Pa, stress in Pa, strain in no unit (a ratio). The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange E = σ / ε?

Rearranging gives these forms: to find Young modulus: E = σ / ε. to find stress: σ = E ε. to find strain: ε = σ / E.

Practise young modulus questions

Include unit conversions (km, g, minutes…)

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Read the full explanation on the Young’s modulus from a test formula page. More materials equations: Stress, Strain. See the full list on the a-level physics equation calculator page.