Calculate mechanical strain (ε = ΔL/L) from the change in length and original length, as a ratio and a percentage. Solve for any missing variable and see the percent elongation directly.
Strain — ε = ΔL / L
How much the object stretched or compressed. Any length unit, as long as it matches the original length.
The unloaded, starting length of the object, in the same unit as ΔL.
Solve for the change in length or original length
Known strain, entered as a percentage (e.g. 0.2 for 0.2%).
Known starting length, in your chosen unit.
Known change in length, in your chosen unit.
Percent elongation — ε × 100
How much the object stretched or compressed, in your chosen unit.
The unloaded, starting length, in the same unit as ΔL.
Result
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Enter values above to compute. Engineering strain is ΔL/L; true strain is ln(Lfinal/L).
3 min read3 steps6 terms3 examples6 FAQsε = ΔL / L
Strain is the most basic way engineers and materials scientists describe how much something deforms under load.
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Walk-through
How to Use This Calculator
3 steps▸
1
Pick a tab for what you know
Use the Strain tab when you know the change in length and the original length and want to find strain. Use the Solve tab when you already know the strain and need to find the missing length. Use the Percent Elongation tab to see the same result framed as a percentage first.
2
Enter your two known values
Change in length (ΔL) and original length (L) can be in any length unit — millimetres, inches, metres — as long as both fields use the same unit. Strain itself is dimensionless, so the unit cancels out of the result.
3
Read the strain and the percent elongation
The result card shows strain as a plain ratio (like 0.002) alongside the equivalent percent elongation (0.2%). The interpretation line below spells out both numbers in one sentence.
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Reference
Formula & Methodology
2 formulas▸
Engineering Strain
ε = ΔL / L
ε (epsilon) is the engineering strain, a dimensionless ratio. ΔL is the change in length (final length minus original length) and L is the original, unloaded length. Both must be in the same unit so it cancels. Example: ΔL = 2 mm, L = 1,000 mm → ε = 2 / 1,000 = 0.002, or 0.2% elongation.
Percent Elongation
% elongation = ε × 100
Multiplying the strain ratio by 100 converts it to a percentage — the more common way strain is reported for ductile materials in tensile testing (e.g. a material rated for 20% elongation before failure).
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Glossary
Key Terms Explained
6 terms▸
Strain ↗The dimensionless ratio of how much an object's length changes relative to its original length: ε = ΔL/L. It has no units because it's a length divided by a length — the same physical stretch reads the same whether measured in millimetres or inches.
Deformation ↗Any change in the shape or size of an object caused by an applied force. Strain is the standardized, size-independent way to measure how much deformation occurred, so a 1 mm stretch on a short rod and a 1 mm stretch on a long rod produce very different strains.
Original Length (L) ↗The unloaded, unstressed starting length of the object before any force was applied — sometimes written L₀. It's the reference length strain is measured against.
Elongation ↗The increase in length of an object under tension, measured as an absolute value (ΔL) or as a percentage of the original length (percent elongation). A negative ΔL represents compression rather than elongation.
Dimensionless ↗A quantity with no physical unit because the units in the numerator and denominator cancel out. Strain is dimensionless because it's a length divided by a length; it's often still written as "mm/mm" or "in/in" for clarity, or expressed as a percentage.
Engineering Strain ↗Strain calculated against the original, undeformed length (ε = ΔL/L), as opposed to true strain, which is calculated against the instantaneous length at each moment of loading. Engineering strain is the standard measure for small deformations and is what this calculator computes.
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Scenarios
Real-World Examples
3 worked examples▸
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Steel Tension Test
Rod stretched under load
Change in length (ΔL) 2 mmOriginal length (L) 1,000 mm
ε = ΔL/L = 2 / 1,000 = 0.002, or 0.2% elongation. A 1-metre steel rod that stretches 2 mm under load has a strain of 0.002 — well within the elastic range for most structural steels, which typically yield around 0.2% strain.
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Solving for the Stretch
Known strain, unknown ΔL
Strain (%) 0.2%Original length (L) 1,000 mm
ΔL = ε × L = 0.002 × 1,000 = 2 mm. If a material spec calls out a 0.2% strain limit and you know the original length, you can work backward to find the maximum allowable stretch.
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Percent Elongation Framing
Same numbers, percent-first view
Change in length (ΔL) 5 mmOriginal length (L) 500 mm
% elongation = (5/500) × 100 = 1%. Reporting strain as a percentage is common in materials datasheets — a ductile material rated for 20% elongation at break can stretch to 20% beyond its original length before fracturing.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
Strain is the most basic way engineers and materials scientists describe how much something deforms under load. Because it's a ratio rather than an absolute measurement, strain lets you compare the stretch of a tiny wire and a massive steel beam on the same scale.
Why Strain Is Measured as a Ratio, Not a Distance
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A 2 mm stretch means very different things depending on what's stretching. Stretch a 10 mm paperclip wire by 2 mm and it has deformed enormously; stretch a 10-metre steel cable by 2 mm and it has barely moved. Strain solves this by dividing the change in length by the original length, producing a dimensionless number that's comparable across any size of object. Because strain is unitless, it's often reported as a plain decimal (0.002), as a percentage (0.2%), or informally as "mm per mm" — all three describe the same physical stretch.
Engineering Strain vs True Strain
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This calculator computes engineering strain — the change in length divided by the original length, which is standard for small deformations in structural and mechanical engineering. There's a related quantity called true strain, which instead divides against the instantaneous length at each point during loading (ε_true = ln(L/L₀)). For small strains (well under 5%), engineering strain and true strain are nearly identical; they diverge meaningfully only for large plastic deformations, such as metal forming or elastomer stretching, where true strain is the more accurate measure.
Compressive Strain and the Sign Convention
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Strain isn't only for stretching. If ΔL is negative — the object got shorter under a compressive load — the strain is negative too, representing compression rather than elongation. The same formula applies either way: enter a negative change in length to compute compressive strain. Strain is the starting point for stress-strain analysis: pair it with the applied force per unit area (stress) and you can find a material's stiffness via Young's modulus, or its safety margin before permanent deformation or failure.
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Questions
Frequently Asked Questions
6 questions▸
What is the formula for strain?+
ε = ΔL / L, where ΔL is the change in length (final length minus original length) and L is the original, unloaded length. Both must use the same length unit.
What units does strain use?+
Strain is dimensionless — it has no units, because a length is divided by a length and the units cancel. It's commonly expressed as a plain ratio (e.g. 0.002) or as a percentage (0.2%).
How do I convert strain to percent elongation?+
Multiply the strain ratio by 100. A strain of 0.002 is 0.2% elongation. This calculator's Percent Elongation tab does this conversion automatically.
Can strain be negative?+
Yes. A negative strain represents compressive strain — the object got shorter under load rather than longer. Enter a negative value for the change in length to compute it.
What's the difference between strain and stress?+
Strain (ε = ΔL/L) measures how much an object deforms — the effect. Stress (force per unit area) measures the internal force causing that deformation — the cause. Dividing stress by strain in the elastic region gives Young's modulus, a measure of material stiffness.
What is true strain, and why doesn't this calculator use it?+
True strain (ε_true = ln(L/L₀)) measures strain against the instantaneous length at each point of loading rather than the fixed original length. It matters mainly for large plastic deformations; for the small strains typical of structural and mechanical engineering, engineering strain (what this calculator computes) is the standard and the two measures are nearly identical.
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