Learn: Poisson's ratio
Pull a bar gently: it usually becomes longer and narrower. Poisson’s ratio compares that sideways strain with the lengthwise strain; it compares relative changes, not the two changes in millimetres.
What the formula is saying
Strain means change in length divided by original length. With tension taken as positive, ordinary lateral contraction is negative, so the minus sign makes the usual Poisson ratio positive.
Read the symbols in plain language
- εlat
- Lateral strain
Signed transverse change/original transverse dimension; contraction is negative.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- εlong
- Longitudinal strain
Signed axial change/original gauge length; it is the nonzero divisor.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- ν
- Result to find
Poisson's ratio. This division compares relative deformations and cancels the strain scale.
ratio / no unit
Sort out the units first
Both inputs must be strains expressed on the same scale: 300 microstrain is 0.0003 and 0.1% is 0.001. The output has no unit because one strain is divided by another.
Assumptions before calculating
Treat the material as homogeneous and linearly elastic, with small strains. Use properties for the actual temperature and loading direction; the calculation is a model of behaviour before yielding, not a failure test.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find ν and explain the result in the stated output unit.
- εlat · Lateral strain
- -0.0003
- εlong · Longitudinal strain
- 0.001
Reverse the lateral-strain sign
The definition contains a minus sign because contraction normally accompanies extension.
-(-0.0003) = 0.0003Divide by longitudinal strain
This division compares relative deformations and cancels the strain scale.
(0.0003) ÷ (0.001) = 0.3
Does this worked answer make sense?
A lateral contraction one third as large as the longitudinal extension gives ν near 0.33. Reversing both strain signs leaves their ratio unchanged.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- εlat · Lateral strain
- -0.0008
- εlong · Longitudinal strain
- 0.002
Reverse the lateral-strain sign
The definition contains a minus sign because contraction normally accompanies extension.
-(-0.0008) = 0.0008Divide by longitudinal strain
This division compares relative deformations and cancels the strain scale.
(0.0008) ÷ (0.002) = 0.4
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
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- εlat · Lateral strain
- -0.00045
- εlong · Longitudinal strain
- 0.0015
Find: Learn: Poisson's ratio
A hint, not the answer
Strain means change in length divided by original length. With tension taken as positive, ordinary lateral contraction is negative, so the minus sign makes the usual Poisson ratio positive.
Both inputs must be strains expressed on the same scale: 300 microstrain is 0.0003 and 0.1% is 0.001. The output has no unit because one strain is divided by another.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Reverse the lateral-strain sign
The definition contains a minus sign because contraction normally accompanies extension.
-(-0.00045) = 0.00045Divide by longitudinal strain
This division compares relative deformations and cancels the strain scale.
(0.00045) ÷ (0.0015) = 0.3
Avoid the common trap
Do not divide lateral displacement directly by longitudinal displacement. Do not delete the contraction sign, and do not mix microstrain with decimal strain.
When this method applies — and when it does not
Longitudinal strain must not be zero. A measured ratio alone does not establish isotropy; for a stable isotropic elastic model, the compatible range is −1 < ν < 0.5. Anisotropic materials need directional properties.
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.
Reading focus: Poisson's ratio. Use the relevant elastic-response, equilibrium, constitutive-relations or shear-and-torsion module; the lesson states its particular sign convention.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.