How to Calculate Percentage Change in Area?

Percentage Change in Area measures how much an area increases or decreases compared with its original value. The calculation uses the difference between the new and original areas divided by the original area. This page covers area-change formulas for rectangles and squares, dimension-based changes, successive changes, reverse percentages and solved numerical examples.

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What Is Percentage Change in Area?

Percentage change in area is the change in area expressed as a percentage of the original area. It is calculated by dividing the change in area by the original area and multiplying by 100.

The formula is Percentage change = [(New area − Original area) ÷ Original area] × 100. A positive result indicates an increase, while a negative result indicates a decrease. For example, if an area changes from 80 cm² to 100 cm², the percentage change is [(100 − 80) ÷ 80] × 100 = 25%.

Percentage Change in Area Video Lessons

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Percentage Change in Area and Perimeter

Learn how to solve percentage-based questions involving changes in the area and perimeter of two-dimensional figures using appropriate mensuration formulas.

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Percentage Change in Area Formula & Tricks

Important Formulas

Basic percentage change in area
Percentage change = [(A₂ − A₁) ÷ A₁] × 100

A₁ is the original area and A₂ is the new area. The result is positive for an increase and negative for a decrease.

Area change when length and breadth change
Net area change (%) = x + y + (xy ÷ 100)

If length changes by x% and breadth changes by y%, use signed values. Take a decrease as a negative percentage.

Equal percentage change in both dimensions
Net area change (%) = 2r + (r² ÷ 100)

When both length and breadth increase by r%, the new area is (1 + r/100)² times the original area.

Reverse percentage for area increase
Original area = Final area ÷ (1 + r/100)

Use this when the final area is known after an r% increase.

Reverse percentage for area decrease
Original area = Final area ÷ (1 − r/100)

Use this when the final area is known after an r% decrease.

Quick Tricks

Use an area multiplier

An increase of r% multiplies the area by 1 + r/100, while a decrease of r% multiplies it by 1 − r/100. This avoids calculating the change separately.

Example: A 20% increase changes an area of 150 cm² to 150 × 1.20 = 180 cm².
Treat dimension decreases as negative values

For a rectangle, substitute negative values in x + y + xy/100 when a length or breadth decreases.

Example: If length increases by 10% and breadth decreases by 10%, net area change = 10 − 10 − 1 = −1%, so the area decreases by 1%.
Remember the square term for two equal increases

If both dimensions increase by r%, the area increase is more than 2r% because the product of the two increases contributes r²/100%.

Example: For a 10% increase in both dimensions, area increase = 10 + 10 + 1 = 21%.

Percentage Change in Area Concepts

Direct Calculation from Original and New Areas

Subtract the original area from the new area, divide by the original area, and multiply by 100.

For an increase, use (new area − original area) ÷ original area × 100. For a decrease, the result is negative; its magnitude gives the percentage decrease. The original area must be used as the denominator, not the new area.

Example: A rectangle changes from 240 cm² to 300 cm². Percentage change = (300 − 240) ÷ 240 × 100 = 25% increase.

Effect of Changing Length and Breadth

If the length changes by x% and the breadth by y%, the area multiplier is (1 + x/100)(1 + y/100).

Expanding the multiplier gives net area change = x + y + xy/100. Use negative values for decreases. If only one dimension changes by r% and the other remains constant, the area changes by exactly r%.

Example: A rectangle has length increased by 20% and breadth decreased by 10%. Net change = 20 − 10 + (20 × −10)/100 = 8%, so the area increases by 8%.

Percentage Change in the Area of a Square

When the side of a square changes by r%, its area changes by 2r + r²/100 percent.

Since area = side², an original side s becomes s(1 + r/100). Therefore, the area multiplier is (1 + r/100)². For a decrease, replace r with −r.

Example: If the side of a square increases from 10 cm to 12 cm, the area changes from 100 cm² to 144 cm². Percentage increase = 44%.

Successive Changes in Area

For two successive area changes of a% and b%, the net percentage change is a + b + ab/100, with decreases represented by negative values.

The rule follows from multiplying the two area factors: (1 + a/100)(1 + b/100). For equal successive decreases, both percentages are negative, so the total decrease is not their simple sum.

Example: A 20% area increase followed by a 10% decrease gives net change = 20 − 10 − 2 = 8% increase.

Finding the Original Area from the Final Area

After an r% increase, divide the final area by 1 + r/100; after an r% decrease, divide it by 1 − r/100.

The reverse calculation uses the factor that produced the final area. It is not correct to subtract or add the same percentage directly to the final area because percentage changes use different bases.

Example: If the final area after a 25% increase is 500 cm², original area = 500 ÷ 1.25 = 400 cm². If 500 cm² is after a 20% decrease, original area = 500 ÷ 0.80 = 625 cm².

Percentage Change in Area Visual Guide & Data

Use the table and chart below to understand the data better.

Area Change for Common Dimension Changes

Calculated percentage changes in the area of a rectangle when its dimensions change.

Length change Breadth change Area change
10% increase 10% increase 21% increase
20% increase 10% decrease 8% increase
10% decrease 10% decrease 19% decrease
15% increase Unchanged 15% increase

Note: Use x + y + xy/100, taking a decrease as a negative percentage.

Square Area Before and After a 10% Side Increase

Visual guide: Square Area Before and After a 10% Side Increase
Original side: 10 units New side: 11 units Original area: 100 square units New area: 121 square units
A square with side 10 units has area 100 square units; increasing the side to 11 units gives area 121 square units, a 21% increase.

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Practice Percentage Change in Area Questions

Practise published questions related to this topic.

1The price of petrol is increased by 28%. A person wants to increase his expenditure by 22% only. By approximately what percent should he decrease his consumption?→ 2An article is sold for Rs. 288 after successive discounts of 20% and 25%. What is the marked price of the article?→ 321.6 ÷ 3.6 × 2 + 0.25 × 16 ÷ 4 - 6 is equal to∶→ 4What is the value of x so that the seven digit number 55350x2 is divisible by 72?→ 5Two articles are sold for Rs. 4,752 each. On one, the seller gains 32% and on the other he loses 28%. What is his overall gain or loss percentage, correct to one decimal place?→ 6The price of sugar is increased by 17%. A person wants to increase his expenditure by 5% only. By approximately what percent should he decrease his consumption?→ 7The value of 15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5 is equal to:→ 8What is the value of x so that the seven digit number 8439x53 is divisible by 99?→ 9Two articles are sold for Rs. 962 each. On one, the seller gains 30% and on the other he loses 26%. What is his overall gain or loss percentage, nearest to one decimal place?→ 10An article is sold for Rs. 288 after successive discounts of 25% and x%. If the marked price of the article is Rs. 480, what is the value of x?→

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Quick Revision Notes

Percentage Change in Area: Revision Points

Use the original area as the base and apply dimension multipliers when the sides change.

  • Percentage change = (New area − Original area) ÷ Original area × 100.
  • For length changes x% and y%, area change = x + y + xy/100.
  • A decrease is written as a negative percentage in dimension and successive-change formulas.
  • If both dimensions increase by r%, area increase = 2r + r²/100%.
  • After an r% increase, Original = Final ÷ (1 + r/100).
  • After an r% decrease, Original = Final ÷ (1 − r/100).
  • A 10% increase followed by a 10% decrease gives a net decrease of 1%, not zero.

Related Topic Explainers

Area of Square → Perimeter of Square → Area of Rectangle → Perimeter of Rectangle → Area of Triangle → Perimeter of Triangle → Heron's Formula → Area of Triangle Using Two Sides and Included Angle →

Percentage Change in Area FAQs

What is the percentage change in area from 50 cm² to 65 cm²?

Percentage change = (65 − 50) ÷ 50 × 100 = 30% increase.

If the length of a rectangle increases by 15% and its breadth remains unchanged, what happens to its area?

The area also increases by 15% because area is directly proportional to length when breadth is constant.

A rectangle's length increases by 10% and breadth increases by 20%. What is the area increase?

Area increase = 10 + 20 + (10 × 20)/100 = 32%.

If both sides of a square decrease by 20%, what is the percentage decrease in area?

Area multiplier = 0.8² = 0.64. Therefore, the area decreases by 36%.

An area increases by 25% and becomes 750 m². What was the original area?

Original area = 750 ÷ 1.25 = 600 m².

An area decreases by 30% and becomes 420 cm². What was the original area?

Original area = 420 ÷ 0.70 = 600 cm².

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