Calculating percentages and percentage change

To find what percentage a value is of another:

Percentage = (Part / Whole) ×100 

Example Questions:

1. A scientist surveys 1,200 people in a town. 750 people have been vaccinated against a virus.

Calculate the percentage of people in this population who are vaccinated.

(750 / 1,200) x 100 = 62.5%

2. A doctor surveys 500 students at a school to find out how many have athlete’s foot.
35 students have athlete’s foot.

Calculate the percentage of students with athlete’s foot.

(35 / 500) x 100 = 7%

Percentage change = (new value−original value / original value) ×100

Or (change / original) x 100

• If the answer is positive, it’s a percentage increase.
• If the answer is negative, it’s a percentage decrease.

Percentage Increase Example:

A plant has a mass of 40g at the start. After 2 weeks it has a mass of 50g.
Calculate the percentage increase in mass.

• Step 1: Find the change: 50g − 40g = 10g
• Step 2: Divide by the original: 10 ÷ 40 = 0.25
• Step 3: ×100: 0.25 × 100 = 25% increase

Percentage Decrease Example 

A leaf contains 20mg chlorophyll before disease. After infection, it contains 1.5mg.
Calculate the percentage decrease in chlorophyll.

• Step 1: Find the change: 20 – 1.5 = 18.5
• Step 2: Divide by the original: 18.5 ÷ 20 = 0.925
• Step 3: × 100: 0.925 × 100 = 92.5% decrease

Practice Question