Last updated: October 2026
How the square root curve works
Short answer: multiply the square root of the original grade by 10 — curved = 10 × √(original), capped at 100. A 64 becomes an 80, a 49 becomes a 70, and a 100 stays 100. Paste your whole class list above and it curves every grade, with class stats and a grade-distribution table.
Square root curve formula — worked example
The formula is one line:
curved = 10 × √(original grade), capped at 100
Take a student who scored 64: √64 = 8, and 10 × 8 = 80 — a 16-point lift. A 49 becomes 10 × 7 = 70. But a 90 becomes 10 × 9.487 ≈ 94.9 — only +4.9. The curve helps low scores the most and barely touches high ones, which is exactly why teachers trust it: the students who struggled get the boost, and nobody can leapfrog a classmate who earned a higher raw score.
Why the square root? It stretches the low end of the scale and compresses the high end. The math guarantee is simple: curving preserves the original rank order — nobody who scored lower raw can end up higher curved.
How to curve a whole class
Switch to the "Grade list" tab above and paste every student's raw score — one per line, or comma-separated. The tool returns each original grade next to its curved grade, plus the class average, min and max before and after, and an A/B/C/D/F distribution so you can see how the class profile shifts. Use Copy results to paste straight into a spreadsheet, or Download CSV for the full table.
Teaching on a different scale? Change the multiplier (default 10). A multiplier of 12 curves more aggressively — but the 100-point cap always applies, so perfect scores stay perfect.
The curve can't save a grade you didn't earn
The most common misunderstanding: that curving guarantees everyone passes. It doesn't — the square root curve preserves rank order, so a 25 becomes a 50 (still failing) while a 64 becomes an 80. Nobody can leapfrog a classmate who earned a higher raw score. The curve is a fairness adjustment for a hard exam, not a rescue plan.
If you're on the student side of the equation, work out the raw score you actually need on the final with the final grade calculator instead of hoping the curve covers the gap. And that "16-point lift" on a 64? It's a 25% jump — see exactly how the percentages stack with the percentage increase calculator.
Frequently asked questions
What is a square root curve?
A square root curve is a grading curve that raises test scores using the formula curved = 10 × √(original grade), with results capped at 100. It lifts low scores the most — a 64 becomes an 80 and a 49 becomes a 70 — while a perfect 100 stays 100. Teachers use it when a test turned out harder than expected and they want to adjust the whole class's scores fairly. It's sometimes nicknamed the "Texas curve" in teacher slang, though the origin of the name isn't documented.
What is the square root curve formula?
Curved grade = 10 × √(original grade), capped at a maximum of 100. For example, 10 × √64 = 10 × 8 = 80. Some teachers use a different multiplier instead of 10 — the calculator above lets you change it — but the shape of the curve stays the same.
When do teachers use a square root curve?
When a test was harder than intended and most students scored lower than their true ability suggests — a mean well below 70 is the classic trigger. It's meant to correct an overly difficult exam, not to hand out free points. If the test was fair and scores are where they should be, most educators advise against curving at all.
Does a square root curve help every student?
No. It helps low and middle scores the most and barely helps high scores — that's by design. A 64 jumps to 80 (+16) while a 90 only rises to about 94.9 (+4.9). Anyone already at 100 gains nothing. Students above ~95 see almost no change, since the curve flattens out near the top.
Is there a cap — can a curved grade go above 100?
No. The formula's result is capped at 100, so curved grades never exceed a perfect score. With the standard multiplier of 10 this only matters conceptually, since 10 × √100 = 100 exactly — but with a custom multiplier above 10 the cap keeps everything at or below 100.
What are alternatives to a square root curve?
The most common is adding a flat number of points to every score (e.g. +10), which treats all students equally but can push scores over 100. Others: dropping the lowest quiz or exam, re-weighting the test's share of the final grade, or grading on a true bell curve (fitting scores to a normal distribution). Each has trade-offs — the square root curve is popular because it's quick, predictable, and never breaks the 100 ceiling.
Can a square root curve ever lower a grade?
No. On a 0–100 scale, 10 × √(original grade) is always equal to or greater than the original grade, so scores can only stay the same or go up — never drop. A raw 0 stays 0 and a 100 stays 100. Because the curve is strictly increasing, the original rank order is preserved: a student who scored lower raw can never end up higher curved than a classmate who outscored them.
Why do you multiply the square root by 10?
Because the square root of a percentage is a number between 0 and 10 (√100 = 10). Multiplying by 10 maps the result back onto the familiar 0–100 grading scale. The 10 is the standard anchor for percentage grades — if your test were on a 50-point scale, the equivalent formula would be √score × √50.
How is a square root curve different from a bell curve?
A square root curve applies the same formula to every score, so no student is compared to their classmates — your curved grade depends only on your own raw score, and the class ranking never changes. A bell curve is relative: it uses the class mean and standard deviation (z-scores) to fit scores to a normal distribution, so a strong class can push a high raw score into a mediocre letter grade. That peer-versus-peer ranking is why bell-curve grading is far more controversial with students and parents.
When should you NOT curve grades?
When the test was fair and scores reflect what students actually know — curving then is just grade inflation. It's also a poor fit when scores are bunched at the top (there's almost nothing left to differentiate), when the class is tiny, or when school policy doesn't allow it. And a curve can't fix a badly written exam: if the questions didn't measure what was taught, re-scoring them won't either.
What about a linear scale — setting the top score to 100?
A linear scale multiplies every score by (100 ÷ highest score), so the top student lands exactly on 100. It works when the whole class scored low on a fair-but-brutal test and you want the top scorer recognized with a perfect mark. The trade-off is the opposite of a square root curve: a linear scale gives high scorers the biggest boost, and if the highest raw score was very low, it can inflate grades wildly. Choose it when the top of the class earned a 100 — choose the square root curve when the students who struggled need the most help.
Is my data private?
Completely. Every calculation happens locally in your browser with JavaScript — your grades are never sent to a server, stored, or tracked in any way.
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