Lateral Strain vs Longitudinal Strain

Physics · Mechanical Properties Of Solids · NEET

When you pull a wire, it gets longer along the pull (that is longitudinal strain, ΔL/L) and thinner across the pull (that is lateral strain, Δd/d). Longitudinal strain is along the applied force; lateral strain is at 90 degrees to it. Memory hook: LONGitudinal = along the LENGTH; LATERal = the LATERAL (side) squeeze. Their ratio (lateral over longitudinal) is Poisson's ratio.
Stretching a wire: two strains at onceoriginallength L, width dstretchedforce (pull) → longitudinalwidth shrinks d→d−Δd (lateral)Longitudinal strain = ΔL/L (along force, +)Lateral strain = Δd/d (across force, −)
Pulling a wire increases its length (longitudinal strain, along the force) and decreases its width (lateral strain, across the force). The two act at 90 degrees and have opposite signs.

Your doubts, answered

Is lateral strain along the force or across it?

Lateral strain is measured ACROSS the force, at 90 degrees to it. If you pull a wire lengthwise, its diameter changes sideways, and that sideways change (Δd/d) is the lateral strain. Longitudinal strain (ΔL/L) is the one measured ALONG the force direction. Students lose marks by swapping these, so fix it: force direction = longitudinal, perpendicular direction = lateral.

Why does a wire get thinner when you stretch it?

The material has (nearly) fixed volume. When you pull it and it gets longer, the atoms rearrange and the wire compensates by shrinking across its width. So longitudinal strain is positive (length increases) while lateral strain is negative (diameter decreases). This sideways shrinking is exactly the lateral strain.

What is the difference in the formulas?

Longitudinal strain = ΔL / L (change in length over original length, along the force). Lateral strain = Δd / d or ΔD / D (change in width/diameter over original width, across the force). Both are ratios of same-type quantities (length/length), so both are pure numbers with NO units and NO dimensions.

Do lateral and longitudinal strain have opposite signs?

Yes, for stretching. Longitudinal strain is positive (length grows) and lateral strain is negative (diameter shrinks). For compression it flips: length shrinks (negative) and width bulges out (positive). Because of this, Poisson's ratio σ = -(lateral strain)/(longitudinal strain) carries a minus sign so that the final value comes out positive.

What is the ratio of lateral strain to longitudinal strain called?

It is called Poisson's ratio, written σ (sigma). σ = -(Δd/d)/(ΔL/L) = -(lateral strain)/(longitudinal strain). This exact ratio was asked in NEET 2026. For most solids σ lies between 0 and 0.5. Learn the limits separately on the Poisson's ratio range page.

⚠️ The NEET trap
Lateral strain and longitudinal strain have different units, so their ratio has units.
Both are length divided by length, so both are dimensionless (no units). Their ratio, Poisson's ratio, is therefore also a pure number.
🧠 NEET loves to test that strain has no unit. Any strain, lateral or longitudinal, is dimensionless. If an option gives strain a unit, it is a trap.

Real NEET questions

NEET 2026

Match List I with List II. List I: A. Young's Modulus, B. Compressibility, C. Bulk Modulus, D. Poisson's Ratio. List II: I. (Δd/d)/(ΔL/L), II. FL/(A·ΔL), III. -(1/V)(ΔV/P), IV. -V·P/ΔV. Choose the correct answer.

A · A-IV, B-I, C-II, D-III
B · A-III, B-II, C-I, D-IV
C · A-I, B-IV, C-III, D-II
D · A-II, B-III, C-IV, D-I
Solution: Poisson's ratio is the ratio of lateral strain (Δd/d) to longitudinal strain (ΔL/L), so D matches I: (Δd/d)/(ΔL/L). Young's modulus = FL/(A·ΔL) = II. Bulk modulus = -V·P/ΔV = IV. Compressibility = -(1/V)(ΔV/P) = III. Therefore A-II, B-III, C-IV, D-I, which is option D. This question directly rewards knowing that lateral strain over longitudinal strain defines Poisson's ratio.

Solved Mechanical Properties Of Solids NEET PYQs

Try the real previous-year questions from this chapter — each with the answer and a full solution.

See all 11 Mechanical Properties Of Solids NEET PYQs ›
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Frequently asked

Which is bigger, lateral strain or longitudinal strain?

Longitudinal strain is bigger in magnitude. Since Poisson's ratio (lateral over longitudinal) is between 0 and 0.5 for real solids, lateral strain is at most half the longitudinal strain, and usually much less.

Can longitudinal strain exist without lateral strain?

Only if Poisson's ratio is zero, which is very rare (like cork). For normal materials, stretching along the length always causes some sideways shrinking, so both strains occur together.

Does lateral strain have a unit?

No. It is a change in width divided by original width, so it is a pure number with no unit and no dimension, exactly like longitudinal strain.

Is lateral strain the same as shear strain?

No. Lateral strain is the sideways change in size when you pull or push along a length (linked to Poisson's ratio). Shear strain is an angle change when a force acts parallel to a surface (linked to shear modulus). They are different ideas.