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Walk-through

How to Use This Calculator

3 steps

1

Pick the tab for what you're solving

Use the Elongation tab to find how much a material stretches under a known load. Use the Percent tab to see that same stretch expressed as a percentage of the original length. Use the Solve tab when you already know the target elongation and need to find the force required to produce it.

2

Enter force, length, area, and Young's modulus

Force (F) is the axial load in newtons, length (L) is the unloaded starting length in millimetres, area (A) is the cross-sectional area in square millimetres, and Young's modulus (E) is the material's stiffness in gigapascals. Steel is about 200 GPa; aluminum is about 69 GPa.

3

Read the elongation and percent elongation

The result card shows the elongation in millimetres alongside the equivalent strain ratio and percent elongation. The interpretation line below spells out the stretch in one sentence.

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Reference

Formula & Methodology

2 formulas

Axial Elongation

ΔL = FL / (AE)

ΔL is the elongation (change in length), F is the applied axial force, L is the original length, A is the cross-sectional area, and E is Young's modulus of the material. This is Hooke's law rearranged for axial deformation — it holds only within the material's elastic range, before it yields. Example: F = 10,000 N, L = 1,000 mm, A = 100 mm², E = 200 GPa → ΔL = (10,000 × 1,000) / (100 × 200,000) = 0.5 mm.

Percent Elongation

% elongation = (ΔL / L) × 100

Dividing the elongation by the original length and multiplying by 100 expresses the stretch as a percentage — the same strain value reported on material datasheets and mill certs (e.g. a steel rated for 20% elongation at break).

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Glossary

Key Terms Explained

6 terms

Elongation The increase in length of a material under an axial tensile load, measured as an absolute distance (ΔL) or as a percentage of the original length. A negative ΔL represents compression rather than elongation.

Axial Deformation A change in an object's length along the direction a force is applied — as opposed to bending, twisting, or shear deformation. ΔL = FL/(AE) describes axial deformation specifically.

Young's Modulus (E) A measure of a material's stiffness in its elastic range: the ratio of stress to strain. A higher Young's modulus means the material stretches less for the same applied stress. Steel (≈200 GPa) is far stiffer than aluminum (≈69 GPa) or rubber (≈0.01–0.1 GPa).

Strain The dimensionless ratio of the change in length to the original length (ε = ΔL/L). Percent elongation is strain expressed as a percentage.

Percent Elongation The elongation expressed as a percentage of the original length: (ΔL/L) × 100. It's the standard way ductility and stretch are reported on material specification sheets.

Tensile Relating to a pulling or stretching force, as opposed to compressive (pushing) or shear forces. This calculator models tensile (stretching) elongation, though the same formula applies to compressive shortening with a negative force.

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Scenarios

Real-World Examples

3 worked examples

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Steel Rod Under Load

Axial tension test

Force (F) 10,000 N Length (L) 1,000 mm Area (A) 100 mm² Young's modulus (E) 200 GPa

ΔL = FL/(AE) = (10,000 × 1,000) / (100 × 200,000) = 0.5 mm. A 1-metre steel rod with a 100 mm² cross-section stretches half a millimetre under a 10 kN axial load — well within steel's elastic range.

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Percent Elongation Framing

Same rod, percent-first view

Force (F) 10,000 N Length (L) 1,000 mm Area (A) 100 mm² Young's modulus (E) 200 GPa

% elongation = (0.5/1,000) × 100 = 0.05%. Reporting the stretch this way makes it easy to compare against a material's rated elongation at break — mild steel typically handles 20%+ elongation before failure, so 0.05% is a tiny fraction of its capacity.

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Solving for the Required Force

Target elongation, unknown force

Elongation (ΔL) 0.5 mm Length (L) 1,000 mm Area (A) 100 mm² Young's modulus (E) 200 GPa

F = ΔL × A × E / L = (0.5 × 100 × 200,000) / 1,000 = 10,000 N. If a design calls for no more than 0.5 mm of stretch on that rod, you can work backward to find the maximum force it can safely carry.

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Deep Dive

Understanding Elongation — ΔL = FL/AE

3 chapters · 3 min read

Elongation is how much a material stretches when you pull on it — the physical answer to "how much does this cable, bolt, or rod actually move under load?" The formula ΔL = FL/(AE) ties that stretch directly to the applied force, the part's geometry, and the material's stiffness.

Where the Formula Comes From

ΔL = FL/(AE) is Hooke's law rearranged for an axially loaded member. Hooke's law states that stress is proportional to strain within a material's elastic range: stress = E × strain, or (F/A) = E × (ΔL/L). Solving for ΔL gives ΔL = FL/(AE). Every variable plays an intuitive role: more force (F) means more stretch; a longer part (L) has more material to stretch, so it stretches more in absolute terms; a larger cross-section (A) spreads the same force over more material, reducing stretch; and a stiffer material (higher E) resists stretching more.

Reading the Result: Absolute vs Percent Elongation

The Elongation tab reports ΔL as an absolute distance — useful when you need to know exactly how much clearance a stretching bolt or cable will consume. The Percent tab reports the same physical stretch as a fraction of the original length, which is how ductility is usually specified on material datasheets (e.g. "minimum 20% elongation at break" for a structural steel). Both numbers describe the same deformation; percent elongation is just the size-independent version, making it comparable across parts of different lengths.

Staying Inside the Elastic Range

ΔL = FL/(AE) is only valid while the material remains elastic — meaning it springs back to its original length if the load is removed. Push the stress (F/A) past the material's yield strength and the relationship breaks down: the material starts to permanently deform (plastic deformation), and this linear formula no longer predicts the actual stretch. In practice, engineers keep the working stress well below yield (see a factor-of-safety calculation) specifically so this formula stays accurate and the part returns to its original shape when unloaded.

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Questions

Frequently Asked Questions

6 questions

What is the formula for elongation?+

ΔL = FL / (AE), where F is the applied axial force, L is the original length, A is the cross-sectional area, and E is Young's modulus of the material. It's Hooke's law rearranged to solve directly for the stretch.

How do I find percent elongation?+

Divide the elongation (ΔL) by the original length (L) and multiply by 100: % elongation = (ΔL/L) × 100. This calculator's Percent tab computes it automatically from the same four inputs.

Does a stiffer material stretch more or less?+

Less. Young's modulus (E) sits in the denominator of ΔL = FL/(AE), so a higher modulus (a stiffer material, like steel at ≈200 GPa) produces less elongation for the same force, length, and area than a more flexible material like aluminum (≈69 GPa).

What units does this calculator use?+

Force in newtons (N), length and elongation in millimetres (mm), cross-sectional area in square millimetres (mm²), and Young's modulus in gigapascals (GPa). The calculator converts internally so the result comes out in millimetres.

How is elongation different from strain?+

Elongation (ΔL) is the absolute change in length. Strain (ε = ΔL/L) is that same change expressed as a dimensionless ratio relative to the original length. Percent elongation is strain multiplied by 100 — so elongation is the raw distance, strain and percent elongation are the size-independent ratio.

Can this calculator solve for the required force?+

Yes. The Solve tab takes a target elongation along with the length, area, and Young's modulus, and solves for the force needed to produce that exact stretch: F = ΔL × A × E / L.

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Elongation Calculator

Elongation — ΔL = FL / AE

Percent elongation — ΔL / L × 100

Solve for the required force

Result

How to Use This Calculator

Pick the tab for what you're solving

Enter force, length, area, and Young's modulus

Read the elongation and percent elongation

Formula & Methodology

Key Terms Explained

Real-World Examples

Steel Rod Under Load

Percent Elongation Framing

Solving for the Required Force

Understanding Elongation — ΔL = FL/AE

Where the Formula Comes From

Reading the Result: Absolute vs Percent Elongation

Staying Inside the Elastic Range

Frequently Asked Questions

Get a branded PDF of your results

Elongation Calculator

Elongation — ΔL = FL / AE

Percent elongation — ΔL / L × 100

Solve for the required force

Result

How to Use This Calculator

Pick the tab for what you're solving

Enter force, length, area, and Young's modulus

Read the elongation and percent elongation

Formula & Methodology

Key Terms Explained

Real-World Examples

Understanding Elongation — ΔL = FL/AE

Where the Formula Comes From

Reading the Result: Absolute vs Percent Elongation

Staying Inside the Elastic Range

Frequently Asked Questions

Get a branded PDF of your results

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