CALCULATOR · SCHOOL · PHYSICS
Stretch a steel bar 0.1% longer and it gets about 0.029% thinner — that trade-off is Poisson’s ratio, ν = −εlateral / εaxial. This solver works three ways: measure both strains to find ν, or give ν plus one strain to predict the other. Default: steel ν = 0.29, axial strain 0.001 in tension → lateral strain −0.00029 (contraction).
Pick what to solve for. From strains: enter the axial and lateral strains you measured and the calculator returns ν. From ν: pick a material preset (or type your own ν) and one strain, and it predicts the other. Tension is positive axial strain; the lateral response carries the minus sign, so ν comes out positive for ordinary materials.
Stretch it, it thins — the ratio is the material. Pull a bar longer and it contracts sideways; squeeze it shorter and it bulges. Poisson’s ratio is the size of that sideways response relative to the pull: ν = −εlateral / εaxial. The minus sign exists because lateral contraction is negative strain under tension — the minus flips it so ν reads positive for ordinary materials. Most metals sit near 0.3; 0.5 means incompressible (rubber); 0 means no sideways response at all (cork); a negative ν means the material gets fatter when stretched (rare auxetics). Default check: −0.29 × 0.001 = −0.00029 — a steel bar stretched 0.1% contracts 0.029% sideways.
Setup: steel, ν = 0.29, axial strain 0.001 (tension).
Line 1 — the formula. εlateral = −ν × εaxial = −0.29 × 0.001 = −0.00029 — a 0.029% contraction, the bar’s diameter shrinking as it lengthens.
Branch — find ν from measured strains: a lab pulls a sample to axial strain 0.002 and measures lateral strain −0.00066. ν = −(−0.00066)/0.002 = 0.33 — aluminum territory (the preset says 0.33). This is exactly how the number is determined in a materials lab: two strain gauges, one division.
Branch — compression: an aluminum rod (ν = 0.33) squeezed to axial strain −0.005. εlateral = −0.33 × (−0.005) = +0.00165 — the rod bulges outward by 0.165% as it shortens. Two minuses make a plus, and the plus is real.
Branch — rubber: ν = 0.49, axial 0.001 → lateral −0.00049 — nearly half the axial strain, because rubber barely changes volume.
Branch — the error case: switch to “Find ν from strains” and set axial strain to 0 — the calculator refuses, because ν = −εlateral/εaxial would divide by zero. Type ν = 0.8 and it refuses that too: outside the −1 to +0.5 theoretical range for isotropic materials.
| Material | ν (typical) | What the number says |
|---|---|---|
| Steel | 0.29 | Everyday metals cluster here — the default on this page. |
| Aluminum | 0.33 | Slightly more lateral give than steel. |
| Copper / brass | 0.34 | Soft metals contract a touch more sideways. |
| Titanium | 0.32 | Strong as steel, a little more lateral response. |
| Glass | 0.22 | Brittle materials thin less under tension. |
| Concrete | 0.20 | Low — concrete barely necks before it cracks. |
| Lead | 0.43 | Soft and dense, approaching rubber territory. |
| Rubber | 0.49 | Near-incompressible: volume barely changes, shape does. |
| Cork | 0.00 | Almost no lateral response — why a wine cork slides in without jamming. |
| Output | Formula | What it means |
|---|---|---|
| Poisson’s ratio ν | −εlateral / εaxial | 0.29 for steel at the defaults — the material’s lateral-to-axial trade-off, dimensionless. |
| Lateral strain | −ν × εaxial | −0.00029 at the defaults — the bar contracts 0.029% sideways (the minus is the point). |
| Axial strain | −εlateral / ν | 0.001 recovered from ν = 0.29 and lateral −0.00029 — the reverse direction, for lab data. |
| Interpretation | class of ν | Typical engineering material at 0.29 — flags auxetic, cork-like, or near-incompressible behavior automatically. |
The formula assumes an isotropic material (same properties in every direction) loaded in the linear elastic range at small strains — wood, composites, and anything past yield need direction-specific or nonlinear treatment, and the ratio can shift with temperature and loading rate. Presets are typical textbook values, not your specimen’s value: steel varies by alloy (0.27–0.30), concrete runs 0.1–0.2, rubber 0.48–0.5. A computed ν outside −1 to +0.5 almost always means a measurement or sign error, not a new material — the calculator flags it.
Bright Side Kit. "Poisson's Ratio Calculator: Strain Solver | Bright Side Kit." https://brightoolbox.com/poissons-ratio-calculator/ Accessed October 24, 2026.Data sourcesBecause of the sign convention. Under tension, axial strain is positive (the bar gets longer) and lateral strain is negative (it gets thinner). Without the minus, ν would come out negative for every ordinary material — annoying. The minus in ν = −εlateral / εaxial flips it so steel reads +0.29 instead of −0.29. In compression both signs flip the same way, and ν is still positive.
The material is incompressible. At ν = 0.5, a stretched bar thins exactly enough to keep its volume constant — the shape changes, the volume doesn’t. Rubber (0.48–0.5) is the classic example: squeeze a rubber eraser and it bulges sideways by just the right amount. It is also the theoretical ceiling for isotropic materials, which is why the calculator treats anything above 0.5 as a likely input error.
Yes — those are auxetic materials. Stretch an auxetic and it gets thicker sideways instead of thinner. Almost nothing in nature does this, but engineered auxetic foams and lattice metamaterials do, and they are used where energy absorption matters — bumpers, protective gear, sneaker soles. If your calculation returns a negative ν for steel or aluminum, though, it is a sign error, not auxetics.
Cork’s cellular structure collapses in place instead of squeezing sideways — push it lengthwise and the cells fold without pushing their neighbors outward. That is exactly why it makes a good wine-bottle stopper: it slides in and out without jamming against the glass the way a rubber stopper (ν ≈ 0.5) would. Enter 0.001 axial strain with ν = 0 and the calculator returns lateral strain 0 — no sideways response at all.
No. Poisson’s ratio is a linear-elastic property: it describes the material only while it springs back when unloaded. Past the yield point, plastic deformation takes over, the relationship between the strains stops being a clean ratio, and metals can show an effective ratio near 0.5 (volume-conserving plastic flow). Keep your strains small and your loads below yield, or the number is meaningless.
None — it is dimensionless. It is a ratio of two strains, and strain itself is ΔL/L — length divided by length. Whether you measure in inches, millimeters, or furlongs, ν = 0.29 for steel. That is why the calculator takes raw strain numbers (like 0.001), not lengths: if you have lengths, divide the change by the original first.
It comes down to how atoms pack. In the dense crystal lattices of common metals, pulling the atoms apart lengthwise lets neighboring rows settle slightly closer together sideways — and the geometry of that settling lands near 0.27–0.34 for steel, aluminum, copper, and titanium alike. It is not a law of nature (concrete is 0.2, lead is 0.44), but it is a deep enough habit that a measured ν of 0.6 on a “steel” sample means you should check the gauges, not rewrite the textbook.