How do I convert marks into a percentage?

Divide the marks you obtained by the total marks available and multiply by 100. If you scored 450 out of 500, that is 450 divided by 500, which gives 0.9, multiplied by 100 for 90 percent. If several papers carry different weightings, calculate the percentage for each and then apply the weighting rather than averaging the raw scores.

Why is percentage increase not the reverse of percentage decrease?

Because each calculation uses a different base. Going from 200 to 250 is a 25 percent increase because the difference of 50 is measured against 200. Going back from 250 to 200 is a 20 percent decrease because the same difference of 50 is now measured against 250. The absolute change is identical but the reference point is not.

How do I work out a discount price?

Subtract the discount percentage from 100 and multiply the original price by that figure divided by 100. For a 30 percent discount on 2,500, multiply 2,500 by 0.70 to get 1,750. To find the discount amount alone, multiply 2,500 by 0.30 to get 750. Where two discounts are applied one after the other, apply them sequentially rather than adding the percentages together.

How do I remove tax from a price that already includes it?

Divide rather than subtract. If a bill of 4,600 already includes 15 percent tax, divide 4,600 by 1.15 to get the pre tax amount of 4,000, and the tax portion is the difference of 600. Subtracting 15 percent from the inclusive figure gives the wrong answer because it applies the percentage to the larger base.

How do I convert marks into a percentage?

Divide the marks you obtained by the total marks available and multiply by 100. If you scored 450 out of 500, that is 450 divided by 500, which gives 0.9, multiplied by 100 for 90 percent. If several papers carry different weightings, calculate the percentage for each and then apply the weighting rather than averaging the raw scores.

Why is percentage increase not the reverse of percentage decrease?

Because each calculation uses a different base. Going from 200 to 250 is a 25 percent increase because the difference of 50 is measured against 200. Going back from 250 to 200 is a 20 percent decrease because the same difference of 50 is now measured against 250. The absolute change is identical but the reference point is not.

How do I work out a discount price?

Subtract the discount percentage from 100 and multiply the original price by that figure divided by 100. For a 30 percent discount on 2,500, multiply 2,500 by 0.70 to get 1,750. To find the discount amount alone, multiply 2,500 by 0.30 to get 750. Where two discounts are applied one after the other, apply them sequentially rather than adding the percentages together.

How do I remove tax from a price that already includes it?

Divide rather than subtract. If a bill of 4,600 already includes 15 percent tax, divide 4,600 by 1.15 to get the pre tax amount of 4,000, and the tax portion is the difference of 600. Subtracting 15 percent from the inclusive figure gives the wrong answer because it applies the percentage to the larger base.

Education

Percentage Calculator

Quick percentage and marks calculator.

Enter details

Pick a mode and enter two numbers

Calculation type

Percentage (P)

Value (X)

Result

20% of 150

How it works

A percentage means "per hundred". The basic formula is:

Part = (Percentage ÷ 100) × Whole
Percentage = (Part ÷ Whole) × 100

This calculation:

20% of 150
= (20 / 100) × 150
= 30

Overview

What is the Percentage Calculator?

A Percentage Calculator handles the everyday maths of proportions: what one number is as a percentage of another, what a given percentage of a value comes to, and how much something has increased or decreased in percentage terms. The word percent simply means per hundred, so a percentage expresses any fraction on a common scale that makes very different quantities easy to compare at a glance.

Percentages appear everywhere in ordinary life. Exam marks, discounts in a sale, interest on a loan, sales tax on a bill, a tip in a restaurant, a pay rise, a commission on a sale, and the change in a price from one month to the next are all expressed as percentages. Doing these calculations in your head is possible but error prone, especially with percentage increase and decrease, where people commonly divide by the wrong base number and get a misleading answer.

Step-by-step

How to use this calculator

1Choose the type of calculation you need, such as percentage of a number, one number as a percentage of another, or percentage change between two values.
2Enter the first value, for example the marks you scored, the original price, or the starting figure.
3Enter the second value, for example the total marks available, the percentage to apply, or the new figure.
4Read the result immediately, along with the working shown so you can check the logic rather than trusting a bare number.
5Adjust either input to compare scenarios, such as how a different discount or a higher score would change the outcome.

Methodology

How it works

Every percentage calculation reduces to a simple ratio multiplied by one hundred. To find what percentage one number is of another, divide the part by the whole and multiply by 100. To find a percentage of a number, divide the percentage by 100 and multiply by the number. Both operations use the same underlying relationship read in different directions.

Percentage change is where most mistakes happen. The correct method is to subtract the original value from the new value, divide that difference by the original value, and multiply by 100. The original value is always the base. This is why a price that rises by 50 percent and then falls by 50 percent does not return to where it started: the second calculation uses the larger figure as its base, so the same percentage represents a bigger absolute amount.

Reference

Common percentage formulas

What you want	Formula	Worked example
X percent of Y	(X / 100) x Y	15% of 4,000 = 600
X as a percentage of Y	(X / Y) x 100	450 out of 500 = 90%
Percentage increase	((New - Old) / Old) x 100	200 to 250 = 25% increase
Percentage decrease	((Old - New) / Old) x 100	250 to 200 = 20% decrease
Add a percentage	Y x (1 + X / 100)	4,000 plus 15% = 4,600
Remove a percentage	Y / (1 + X / 100)	4,600 including 15% = 4,000 before

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