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Grade Curve Calculator

Adjust test percentages with an add-points, square-root, highest-score, target-average or z-score method. Compare every original score with its curved result.

How to use the grade curve calculator

Enter percentage scores. Paste one score or up to 500, separated by commas, spaces or new lines. For raw marks, first divide marks earned by marks available and multiply by 100. For example, 36 out of 50 is 72%.
Select the curve method. Enter an adjustment, target average or target standard deviation if the selected method needs one. For methods based on class performance, include the entire class.
Choose the maximum. Keep the 100% cap selected unless your course permits adjusted scores above 100%. A minimum of 0% always applies.
Calculate and compare. View the original average, adjusted average and change for every score. Download the results as CSV if you want to keep a copy.

Load example fills in five sample scores. Changing an input hides the previous result until you calculate again. Reset clears the scores and restores the default settings.

Curve your test scores

Compare original and adjusted percentages using a method chosen by your instructor.

Grade curve formulas and methods

In these formulas, x is an original percentage and y is the adjusted result before the 0% floor and optional 100% cap. Keep full precision during calculation; displayed results use two decimals.

Add percentage points

y = x + a

Add the same adjustment, a, to every original percentage, x. With a five-point adjustment, 70% becomes 75%. A negative adjustment lowers scores. Five percentage points is different from a 5% relative increase.

Add points so the highest score becomes 100%

y = x + (100 − H)

H is the highest entered percentage. If the highest score is 90%, add 10 percentage points to everyone. A score of 60% becomes 70%.

Scale the highest score to 100%

y = (x ÷ H) × 100

Divide each score by the highest entered score and multiply by 100. With a highest score of 90%, a score of 60% becomes 66.67%. This proportional method differs from adding ten points. It cannot be used when every score is zero.

Square-root curve

y = 10 × √x

Use x on the 0–100 percentage scale. A score of 64% becomes 80%, while 81% becomes 90%. Zero remains zero and 100 remains 100. This formula gives a larger percentage-point boost to 25% than to 81%; the boost is not simply largest at the lowest possible score.

Shift to a target class average

y = x + (T − μ)

T is the desired average and μ is the mean of the original scores. If the original average is 70% and the target is 75%, add five percentage points to each score. Capping or flooring results can prevent the adjusted average from reaching the target.

Z-score scaling

z = (x − μ) ÷ σ; y = T + z × S

The calculator uses the population standard deviation σ of the entered scores, dividing squared deviations by the number of scores. T is the target average and S is the target standard deviation. Before limits are applied, this changes the mean and spread. It does not make a skewed distribution bell-shaped or assign fixed proportions of letter grades. Two or more different scores are required.

Example: compare different curves

Suppose a class has scores of 50, 60, 70, 80 and 90%. Its average is 70% and its highest score is 90%. Here is how the student with 60% would fare:

Method	Setting	Adjusted score
Add points	+5 percentage points	65.00%
Highest-to-100 addition	Add 100 − 90	70.00%
Highest-to-100 scaling	60 ÷ 90 × 100	66.67%
Square root	10 × √60	77.46%
Target average	Target 75%	65.00%
Z-score scaling	Target mean 75, SD 10	67.93%

Why the achieved average can differ

For scores of 80 and 100, the original average is 90%. Shifting to a target of 100% produces 90 and 110 before limits. With the 100% cap enabled, the results become 90 and 100, so the achieved average is 95%. The calculator reports the actual adjusted average and flags scores affected by a limit.

Does a curve always improve a grade?

No. A negative point adjustment, a lower target average or z-score scaling can lower some results. The appropriate method depends on the instructor’s policy. These calculations are comparisons, not a prediction of an official grade.

Grade Curve Calculator FAQs

How do I calculate a curved grade?

Choose the method your instructor uses, then apply its formula to the original percentage. For example, adding five percentage points changes 72% to 77%. A square-root curve changes 64% to 80%. Different methods can give different results for the same score.

How do I curve a test to the highest score?

There are two distinct methods. Add 100 minus the highest percentage to every score, or divide each score by the highest percentage and multiply by 100. With a high of 90%, a score of 60% becomes 70% by addition or 66.67% by proportional scaling.

What is a square-root grade curve?

This calculator uses 10 times the square root of the original percentage. For 49%, the result is 70%. Enter percentages on the 0–100 scale, not decimal proportions such as 0.49 for 49%.

Can I calculate a bell curve with the class average?

An average alone is not enough for z-score scaling: the spread of the scores matters too. Enter the class scores and choose Z-score scaling to calculate the original mean and population standard deviation. This changes the mean and spread but does not force a normal distribution or award letter grades by rank.

What happens when all students have the same score?

Z-score scaling is undefined because the standard deviation is zero, so the calculator asks for different scores. You can still use addition, square root or a target-average shift. Highest-score scaling requires the common score to be greater than zero.

Use your curved score in your course grade

Once your instructor confirms the adjusted percentage, use the Weighted Grade Calculator for category weights, or the Grade Calculator for points and averages. To work out a required exam score, use the Final Grade Calculator.