Normal Strain (ε = δ/L)
Worked example: 2 mm over 4 m → 500 microstrain — press Try an example to run it live, then adjust anything.
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Normal Strain (ε = δ/L) explained
Strain is stretch per unit of original length, so it carries no units at all — a 2 mm elongation over a 4 m member is ε = 0.002 ÷ 4 = 0.0005, or 500 microstrain. Engineers quote microstrain (µε, parts per million) because real elastic strains are tiny: steel yields at roughly 1200 µε, barely a millimetre per metre. Measuring numbers that small was impossible until 1938, when Edward Simmons at Caltech and Arthur Ruge at MIT independently glued fine wire to a specimen and watched its electrical resistance change — the bonded foil strain gauge, still the backbone of every load cell and truck scale today.
The trap is the denominator: strain is always referred to the original length, not the stretched one. Divide by the final length and you have computed "true strain", which differs from engineering strain by less than a tenth of a percent in the elastic range but diverges wildly once a tensile specimen starts necking. Keep both lengths in the same unit and the ratio takes care of itself.
Normal Strain (ε = δ/L) formula
- = Normal strain (m/m)
- = Change in length (m)
- = Original length (m)
Missing one of these? Work it out first, then come back
- Normal strain — Young's Modulus (E = σ/ε), Shear Modulus (G = τ/γ)
- Change in length — Thermal Linear Expansion, Rectangle Perimeter
- Original length — Axial Deformation (δ = PL/AE), Thermal Linear Expansion