To do ratios on Desmos, type the ratio as a fraction, such as 4320/2400, and Desmos shows its value, 1.8. For a proportion, graph each side and read where they cross. For percentages, multiply by the decimal (25% becomes 0.25), or use the % key, which Desmos reads as "percent of."
Short answer: most of the work in a ratio or percent question is arithmetic, and Desmos does it for you. The steps below show how to do ratios on Desmos and how to work percentages, each on a question from our 2026 banks. For more Desmos techniques, start at our Desmos SAT hub.
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Question banks: October 2026 Math question bank
Notes and practice need a free account: one click with Google, and you land straight on the lesson.
Where do ratios and percentages show up on the SAT?
These moves work on Digital SAT-style percent questions. Start with free lesson notes and Targeted Practice, no card needed.
Start 1-day free trial →They are part of Problem-Solving and Data Analysis, one of the four Math domains. College Board's Assessment Framework (version 4, September 2026) lists "Ratios, rates, proportional relationships, and units" and "Percentages" as skills in that domain. The same document says the domain is about 15% of scored SAT Math questions, or 5 to 7 questions.
The Desmos calculator is built into Bluebook for the whole Math section, so you can use it on all of them. Not sure about the rules? Read is Desmos allowed on the SAT.
How to do ratios on Desmos: 3 moves
A ratio compares two amounts, like 18 to 10. On Desmos, you type a ratio as a division.
- Find a unit rate. Type the top number, a slash, then the bottom number. 4320/2400 gives 1.8. That means 1.8 of the first amount for every 1 of the second.
- Check a table for a constant ratio. Put the table into Desmos (type "table" on a new line). Then type y1/x1 as the header of a third column. The Desmos tables guide says: "If a column header contains a calculation, the column will fill with the computed values." If every value in the new column is the same, the relationship is proportional.
- Solve a proportion. For 3/5 = x/40, graph y = 3/5 and y = x/40 on two lines. Click where they cross. The point is (24, 0.6), so x = 24. This is the same crossing-point method from our guide on how to solve for x on Desmos.
Worked example: a ratio question from the October 2026 SAT
This question is from the October 2026 SAT Math Question Bank (Algebra, Linear Functions, rated Intermediate in our bank).
The roofs on the buildings of a public garden are designed to allow water to drain into the garden. The table shows the relationship between the area x, in square feet, of a roof and the amount of water f(x), in gallons, drained from the roof into the garden over a certain period of time. Which equation could define f?
| Area (square feet) | Water (gallons) |
|---|---|
| 2,400 | 4,320 |
| 3,600 | 6,480 |
| 4,800 | 8,640 |
A) f(x) = 0.6x B) f(x) = 1.8x C) f(x) = 2,160.0x D) f(x) = 4,320.0x
On Desmos: make a table with the areas in x1 and the gallons in y1. Add a third column with the header y1/x1. Every row shows 1.8.
Show the answer
Answer: B) f(x) = 1.8x. 4,320 ÷ 2,400 = 1.8, 6,480 ÷ 3,600 = 1.8, and 8,640 ÷ 4,800 = 1.8. The ratio of gallons to square feet is the same in every row, so f(x) = 1.8x. Check choice D: at x = 2,400 it gives more than 10 million gallons, not 4,320.
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How to do percentages on Desmos
There are two ways to type a percent. Both give the same answer.
- The decimal way. A percent is a number out of 100. So 25% of 288 is 0.25 × 288 = 72. Type 0.25*288.
- The % key. Desmos's own API changelog calls % the "percent of" operator. Tutor guides describe what you see: Acely's Desmos cheat sheet says if you enter a number with a % sign, "Desmos will generate the text 'of' and wait for an input." So typing 25% then 288 reads as 25% of 288.
| SAT percent question | What to type in Desmos | Example |
|---|---|---|
| What is 25% of 288? | 0.25*288 | 72 |
| 84 is 35% of what number? | Graph y = 0.35x and y = 84, click the crossing | x = 240 |
| Percent change from old to new | (new − old)/old*100 | 64 to 68 gives 6.25 |
| A value becomes k times as big. Percent increase? | (k − 1)*100 | 3.41 times gives 241 |
| Ratio of two amounts | first/second | 4320/2400 gives 1.8 |
Worked example: percent change (September 2026 SAT)
From the September 2026 SAT Math Question Bank (Percentages, rated Intermediate, fill-in answer):
The price of an item increased by p% from $64 to $68. What is the value of p?
On Desmos: type (68 − 64)/64*100.
Show the answer
Answer: 6.25. The change is 68 − 64 = 4. Divide by the starting price: 4 ÷ 64 = 0.0625. Multiply by 100 to get 6.25. If you divide by the new price, 68, you get about 5.88, which is wrong.
Worked example: percent increase from a multiplier (October 2026 SAT)
Also from the October 2026 bank (Percentages, rated Hard):
At a hotel, guests used the pool for a total of t hours in March. At the same hotel, guests used the pool for 3.41t hours in April. What is the percent increase in the number of hours guests used the pool from March to April?
A) 2.41% B) 3.41% C) 241% D) 341%
On Desmos: pick any value for t, like 100. Then April is 341. Type (341 − 100)/100*100.
Show the answer
Answer: C) 241%. The new amount is 3.41 times the old one. The increase is 3.41t − t = 2.41t, which is 241% of t. Choice D, 341%, is the trap. It is the new amount as a percent of the old one, not the increase.
Picking a number for a letter, as we did with t = 100, works when the answer does not depend on that letter, as here. Use 100 so the percent is easy to read.
Common mistakes with ratios and percents on Desmos
- Dividing by the wrong amount. Percent change divides by the starting value.
- Mixing up "percent of" and "percent increase." 341% of a number is a 241% increase.
- Flipping a ratio. "Gallons per square foot" is gallons divided by square feet. Read the units in the question.
- Typing the % sign where you meant a decimal. If the % key gives you a result you did not expect, retype it as a decimal.
Some ratio questions are faster by hand, such as 50% of a number. See when not to use Desmos on SAT math. When the table is not a clean ratio, a regression may be the right tool: read when to use regression on the SAT.
Where to practice ratios and percentages
- Free lesson notes. TTA's Percent Change lesson notes and Rates, Unit Conversions and Ratios lesson notes teach one skill at a time. A free account is needed to open them.
- More worked percent problems. Read SAT percent change practice and SAT percent questions: increase, decrease and multi-step.
- Question bank practice. The examples above come from the October 2026 and September 2026 Math banks. All banks are on our SAT question bank page.
- Timed practice. Create a free account to take one full-length adaptive SAT section free. You get a real Module 1 to Module 2 route and a scaled score. You can also browse all Digital SAT practice tests.
How we built this page
Desmos steps come from the Desmos Help Center (Tables) and the Desmos API changelog; the % key description is quoted from Acely's Desmos cheat sheet and labeled as such. SAT domain facts come from College Board's Assessment Framework for the Digital SAT Suite, version 4. The three example questions come from The Test Advantage's October 2026 (database test 4235, questions 758201 and 758332) and September 2026 (test 2915, question 568889) SAT Math banks. For each, we read the keyed answer in our database and solved it again by hand; all three matched. Verified 2026-10-13.
Frequently Asked Questions
How do you type a ratio in Desmos?
Type it as a division with a slash, such as 4320/2400. Desmos shows the value, 1.8, which is the unit rate: 1.8 of the first amount for each 1 of the second.
How do you check if a table is proportional on Desmos?
Enter the table, then type y1/x1 as the header of a new column. The Desmos tables guide says a column with a calculation in its header fills with computed values. If every value is the same, the relationship is proportional.
How do you do percentages on Desmos?
Change the percent to a decimal and multiply, so 25% of 288 is 0.25*288 = 72. Desmos also treats the % key as a percent-of operator, so 25% followed by 288 means 25% of 288.
How do you find percent change on Desmos?
Type (new - old)/old*100. For a price that rose from 64 dollars to 68 dollars, that is (68 - 64)/64*100 = 6.25, so the price rose 6.25%.
What is the difference between 341% of a number and a 341% increase?
341% of a number is 3.41 times it, which is a 241% increase. A 341% increase would make the number 4.41 times as big. In an October 2026 SAT bank question, 341% is the trap choice.