{
    "name": "Poisson’s Ratio Calculator",
    "url": "https://calculators.geekmidst.com/calculators/poisson-ratio-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/poisson-ratio-calculator.md",
    "category": "Science & engineering",
    "description": "Calculate Poisson’s ratio ν = −ε_lateral ÷ ε_axial from dimension changes or measured strains, plus volumetric strain and shear and bulk moduli from E.",
    "summary": "Stretch a bar and it gets thinner. Poisson’s ratio is how much: ν = −(lateral strain) ÷ (axial strain), about 0.3 for most metals.",
    "also_called": [
        "Poisson’s ratio calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "mode",
            "label": "I have",
            "type": "segmented",
            "default": "dimensions",
            "options": {
                "dimensions": "Dimension changes",
                "strains": "Strains"
            }
        },
        {
            "name": "l0",
            "label": "Original length",
            "type": "number",
            "default": "100",
            "unit": "mm",
            "shown_when": {
                "mode": "dimensions"
            }
        },
        {
            "name": "dl",
            "label": "Change in length (+ longer)",
            "type": "number",
            "default": "0.1",
            "unit": "mm",
            "shown_when": {
                "mode": "dimensions"
            }
        },
        {
            "name": "d0",
            "label": "Original width or diameter",
            "type": "number",
            "default": "10",
            "unit": "mm",
            "shown_when": {
                "mode": "dimensions"
            }
        },
        {
            "name": "dd",
            "label": "Change in width (− thinner)",
            "type": "number",
            "default": "-0.003",
            "unit": "mm",
            "shown_when": {
                "mode": "dimensions"
            }
        },
        {
            "name": "axial",
            "label": "Axial strain",
            "type": "number",
            "default": "0.001",
            "shown_when": {
                "mode": "strains"
            }
        },
        {
            "name": "lateral",
            "label": "Lateral strain",
            "type": "number",
            "default": "-0.0003",
            "shown_when": {
                "mode": "strains"
            }
        },
        {
            "name": "e",
            "label": "Young’s modulus E (optional)",
            "type": "number",
            "default": "200",
            "unit": "GPa",
            "optional": true
        }
    ],
    "outputs": [
        {
            "key": "nu",
            "label": "Poisson’s ratio ν",
            "format": "decimal4"
        },
        {
            "key": "axial_strain",
            "label": "Axial strain",
            "format": "number"
        },
        {
            "key": "lateral_strain",
            "label": "Lateral strain",
            "format": "number"
        },
        {
            "key": "volumetric_strain",
            "label": "Volumetric strain (small-strain)",
            "format": "number"
        },
        {
            "key": "shear_modulus",
            "label": "Shear modulus G",
            "format": "text"
        },
        {
            "key": "bulk_modulus",
            "label": "Bulk modulus K",
            "format": "text"
        }
    ],
    "formula": {
        "text": "ν = −ε_lat ÷ ε_ax;  ε_v ≈ ε_ax + 2 ε_lat;  G = E ÷ (2(1 + ν));  K = E ÷ (3(1 − 2ν))",
        "variables": {
            "ε_ax": "axial strain ΔL ÷ L₀",
            "ε_lat": "lateral strain Δd ÷ d₀",
            "E": "Young’s modulus",
            "G": "shear modulus",
            "K": "bulk modulus"
        }
    },
    "worked_example": {
        "inputs": {
            "mode": "dimensions",
            "l0": "100",
            "dl": "0.1",
            "d0": "10",
            "dd": "-0.003",
            "axial": "0.001",
            "lateral": "-0.0003",
            "e": "200"
        },
        "steps": [
            "ε_ax = 0.1 ÷ 100 = 0.001.",
            "ε_lat = −0.003 ÷ 10 = −0.0003.",
            "ν = −(−0.0003) ÷ 0.001 = 0.3.",
            "G = 200 ÷ (2 × 1.3) = 76.92 GPa."
        ],
        "result": "A 100 mm bar stretching 0.1 mm while its 10 mm diameter shrinks 0.003 mm has ν = 0.30, typical of steel."
    },
    "interpretation": "Most metals sit at 0.25–0.35, rubber close to 0.5 (nearly incompressible), cork near 0. A value outside −1 to 0.5 means a sign or measurement error for an isotropic material.",
    "assumptions": [
        "Isotropic, linear-elastic material under uniaxial load; small strains."
    ],
    "limitations": [
        "Anisotropic materials (wood, composites, single crystals) have several Poisson’s ratios depending on direction."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why the minus sign?",
            "answer": "Lateral strain is normally opposite in sign to axial strain, so the minus sign makes ν positive for ordinary materials."
        },
        {
            "question": "Can ν be negative?",
            "answer": "Yes, for auxetic materials such as some foams and engineered lattices, which get wider when stretched."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Young’s Modulus, Stress and Strain Calculator",
            "url": "https://calculators.geekmidst.com/calculators/young-modulus-strain-calculator"
        },
        {
            "name": "Torsion Stress Calculator",
            "url": "https://calculators.geekmidst.com/calculators/torsion-stress-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}