How to calculate strain from a change in length
Strain measures the change in length relative to the starting length. A 2 mm extension is a much bigger change for a short sample than for a very long one.
What the formula is saying
First find the change, final length minus original length. Then divide that change by the original length. The two length units cancel, leaving a dimensionless ratio.
Read the symbols in plain language
- ΔL
- Change in lengthm
- L
- Original lengthm
Sort out the units first
Both lengths must use the same unit. Here 2 mm = 0.002 m and the original length is 2 m. A strain of 0.001 equals 0.1%, not 0.001%.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- ΔL · Change in length
- 0.002 m
- L · Original length
- 2 m
Identify the change, not the final length
Δ means “change in”. Extension is positive in this example.
(0.002) = 0.002 mCompare with the original length
Divide by the length before the rod stretched.
(0.002) ÷ (2) = 0.001
Does this worked answer make sense?
The answer should be small when the extension is tiny compared with the starting length. Multiply by 100 only when reporting a percentage.
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Use these new values. Work it out first, then check your answer.
- ΔL · Change in length
- 0.003 m
- L · Original length
- 1.5 m
Find: strain from a change in length
A hint, not the answer
First find the change, final length minus original length. Then divide that change by the original length. The two length units cancel, leaving a dimensionless ratio.
Both lengths must use the same unit. Here 2 mm = 0.002 m and the original length is 2 m. A strain of 0.001 equals 0.1%, not 0.001%.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Identify the change, not the final length
Δ means “change in”. Extension is positive in this example.
(0.003) = 0.003 mCompare with the original length
Divide by the length before the rod stretched.
(0.003) ÷ (1.5) = 0.002
Avoid the common trap
Do not divide by the final length for this engineering-strain definition. Do not enter millimetres in one field and metres in the other.
When this method applies — and when it does not
Engineering normal strain, not logarithmic true strain. Negative change represents shortening with this sign convention.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.