Percentile to Percentage Converter

Convert an exam percentile to an estimated percentage of marks, or a percentage to a percentile, using the exam’s average and spread or its own table.

• All Statistics Calculators
• GATE Percentile Calculator
• Marks Percentage Calculator
• 10th Percentile Calculator
• Z-Score Calculator
• IQ Percentile Calculator

Calculator Functions

A percentage is your marks out of the maximum. A percentile is your position among the candidates. One does not turn into the other by a fixed formula, so the converter works from what is known about the exam.

With a percentile alone, the result shows the share of candidates you finished ahead of. To get a percentage from marks, use the Marks Percentage Calculator. To get a percentile from a rank, use the GATE Percentile Calculator, and to find a percentile in a list of scores, the 10th Percentile Calculator.

Percentile to Percentage Formulas

These formulas treat the marks as a normal distribution, the bell curve, whose location is the average and whose scale is the standard deviation [1]. Going from a percentile to a percentage, the calculator finds the z that has P% of the curve below it, then applies the first line. Neither Φ nor its reverse has a simple closed formula, so both are computed numerically [1].

For a percentile of 92.5 in an exam that averaged 58% with a standard deviation of 14, z = 1.44 and S = 58 + 1.44 × 14 = 78.2%. On a paper marked out of 300 that is about 234.5 marks. In reverse, 85% in an exam that averaged 60% with a standard deviation of 15 gives z = (85 − 60) ÷ 15 = 1.67, the 95.22 percentile.

Percentile and percentage measure different things

A percentage is marks obtained ÷ maximum marks × 100. A percentile rank is the percentage of test takers who earned your score or lower [3]. For a set of measurements, the pth percentile is the value with at most that share of the measurements below it, and the 50th percentile is the median [2]. So a percentile of 90 means you did as well as or better than 90% of the candidates, whatever your marks were. In a hard paper that can be 60% of the marks, and in an easy one 95%.

The one thing a percentile fixes is your place. With P as the percentile, 100 − P percent of candidates scored higher. At a percentile of 99.2 among 1,100,000 candidates, 0.8% of them, about 8,800, are ahead of you.

Using the exam's own table

When the exam body publishes marks at several percentiles, or you can collect them from score cards, that table is the exam's real distribution and beats any bell curve. The calculator finds the two rows on either side of your value and reads between them on a straight line. P₁, M₁ and P₂, M₂ are the percentile and marks of those rows. With rows of 90 percentile = 152 marks and 95 percentile = 168 marks, a percentile of 92.5 gives M = 152 + 2.5 ÷ 5 × 16 = 160 marks. The same line run the other way turns marks into a percentile.

Limits of This Estimate

• The bell curve is an assumption. Real exam marks are often lopsided and can't pass the maximum, so the estimate is weakest near the top and bottom percentiles. These estimates are based on the best available data and estimations.
• The result depends on the average and standard deviation you enter. If the exam body doesn't publish them, use its percentile table, or treat the answer as a rough guide.
• The table function draws a straight line between rows. Rows that are far apart give a rougher answer than rows close to your value.
• Exam bodies count percentiles in slightly different ways, and some scale or normalize marks first. Only the exam body's own result is official.

Sources