Ratio Calculator

Ratio Calculator: Simplify Any Ratio or Solve a Specific Use Case

This ratio calculator has two functions. You give it two or three numbers and it puts them in their simplest form, a whole number. Or pick a use-case tab and it’ll apply the exact formula you need, aspect ratio for displays and video, gear ratio for bikes and machines, debt-to-income ratio for a mortgage application, the “golden ratio” for design work, or waist-to-height ratio as a general health metric.

Those five items seem unrelated and they are in practice. There is nothing in common between a video editor and a mortgage application. But behind all of them, they’re all doing the same thing: taking a pair of numbers and telling you how they relate to each other in a simpler way. But when you learn that basic procedure in the part below, every specific use case is a brief extra step instead than a full new talent. Each section below stands on its own, so go right to the one you came for.

How to Calculate Ratio (Simplifying the Basics)

A ratio calculator compares two quantities. Written as a:b, it tells you how much of one thing there is relative to another.

To simplify a ratio, you find the greatest common divisor (GCD), which is the largest number that divides evenly into both sides, then divide both sides by it.

Worked example: simplify 24:36

1. List what divides into 24: 1, 2, 3, 4, 6, 8, 12, 24
2. List what divides into 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
3. The biggest number on both lists is 12. That is your GCD.
4. Divide both sides: 24 ÷ 12 = 2, and 36 ÷ 12 = 3
5. Simplified ratio: 2:3

That means for every 2 of the first thing, there are 3 of the second. The relationship has not changed, only the presentation.

A faster way for massive numbers. Instead of mentioning factors divide the larger number by the smaller and save the residue. Repeat the process using the preceding divisor until the remainder is zero. Your GCD is the last nonzero number. For 1920 and 1080: 1920 ÷ 1080 leaves 840, 1080 ÷ 840 leaves 240, 840 ÷ 240 leaves 120, 240 ÷ 120 leaves 0. The GCD is 120.

Ratios of three numbers are the same. 12:18:24, and then 6 is the GCD for all 3 so you get 2:3:4.

Ratios and fractions are close relatives. The ratio 2:3 and the fraction 2/3 employ the same arithmetic but solve different queries. The ratio compares two parts with each other. A fraction tells how much of anything there is compared to a whole. Say in a class there are 2 girls for every 3 boys; the ratio is 2:3. Girls are 2/5 of the class.

Aspect Ratio Calculator (and Screen Ratio)

By measuring a rectangle’s width to its height, aspect ratio shows what shape it has. It’s written as width:height. For displays, “screen ratio” and “ratio” mean the same thing, so the two terms can be used instead of each other.

Worked example 1: find the aspect ratio of a 1920×1080 image

• 1920 pixels wide and 1080 pixels tall.
• Based on what you learned above, the GCD of 1920×1080 is 120.
• 1920 x 120 is equal to 16, and 1080 x 120 is equal to 9.
• The ratio is 16:9.

Every screen that is 1920×1080, 3840×2160, or 1280×720 is 16:9. Different number of pixels, same shape.

Worked example 2: scale a known ratio to a new size

Allow us to say that the width of your website is 1200 pixels and you need a 16:9 movie to fit perfectly.

• Heights are equal to width times (height divided by width).
• Height = 1200 × (9 x 16)
• Height = 1,200 divided by 0.5625
• Size = 675 pixels high

A rectangle that is 1200×675 is a perfect 16:9 size. That’s right, if you know the height and need to find the width, increase the height by 16 ÷ 9.

Common aspect ratios and where you will meet them:

Why it matters in practice. Upload a 4:3 video to a 16:9 player and you get black bars down each side. Force a 16:9 image into a square crop and you lose a third of the picture. Matching the ratio to the destination before you export saves the re-edit.

Gear Ratio Calculator

Gear ratio is a way of expressing how many times the driving gear has to turn to turn the driven gear once. It applies to automobile transmissions, bicycles, drill motors, clocks, and anything else that transfers rotation.

Gear Ratio = (Number of Teeth in Driven Gear) / (Number of Teeth in Driving Gear)

The drive gear is the gear attached to the power source. The driven gear is the one that receives it.

Worked example: 40-tooth driven gear, 10-tooth driving gear

• 40 ÷ 10 = 4 
• As a ratio this is written 4:1

Meaning: the little driving gear makes 4 full rotations for every turn of the big driven gear

Trade off speed vs. torque. A ratio of 4:1 is a decrease. The output shaft rotates 4 times slower than the input. 

It also delivers roughly 4 times the torque ( ignoring losses due to friction). That’s the deal every gearbox gets. You don’t get greater power and more speed out of the same engine at the same time. You choose the one you want.

Do the maths on a motor spinning at 1,200 rpm thru that 4:1 reduction.

• Output speed = 1200/4 = 300 r.p.m.
• The output torque is around four times the input torque.

Turn it over and you have overdrive. Use 20 tooth gear as driven and 40 tooth as driving and the ratio becomes 20 ÷ 40 = 0.5 or 1:2. Now the output spins twice as rapidly as the input, but with only half the torque. This is what the highest gear of your car does on a motorway and what the biggest chainring and smallest rear cog of a bike do on a descent.

Quick intuition test. Big driving gear = higher torque less speed. Small driving gear = more speed, less torque. If you get your result inverted, you probably switched driving and driven in the formula.

How to Calculate Debt to Income Ratio

Your debt-to-income ratio, or DTI, is the percentage of your gross monthly income that goes toward debt payments. Lenders utilise this to figure out how much more debt you can reasonably afford to accept on top of the debt you already have.

DTI (%) = Total Monthly Debt Payments Gross Monthly Income* X 100

Worked example: $6000 gross monthly income, $1800 debt payments

• 1,800 ÷ 6,000 = 0.30 
• 0.30 x 100 = 30% DTI

Use gross, not net. Gross is before taxes and deductions. This is a common pitfall and utilising your net pay will make your DTI look a whole lot worse than the number a lender comes up with.

• What is considered debt in this calculation?
• Rent or mortgage payment
• Payments on a car loan or lease
• Paying back student loans
• Credit Card Minimum Payments
• Personal loan repayments
• Child support or alimony ordered by a judge

What doesn’t count: groceries, utilities, phone bills, insurance premiums, streaming subscriptions, petrol, or anything else that is a living expense, rather than a financial obligation.

What Lenders Want. A DTI of 36% or below is frequently cited as a comfort zone. The 43% had been the long-standing benchmark for a typical qualified mortgage in the US, however the Consumer Financial Protection Bureau has subsequently replaced that hard restriction for the general category with price-based requirements. Many lenders will still approve above 43% based on your credit score, savings and deposit amount and certain loan programs go higher again.

Treat them as reference points, not rules. Thresholds depend on the lender, the type of loan and the country. And a lender approving you at 45% does not mean 45% is pleasant to live with.  That is a different subject and only your own budget can answer that.

Golden Ratio Calculator (Also Called the Divine Ratio)

The “golden ratio” is denoted by the Greek letter φ (phi) and is roughly 1.618. It defines a particular manner of dividing a line. The ratio of the whole to the bigger part is equal to the ratio of the larger part to the smaller part.

Thus whole ÷ larger equals larger ÷ smaller both equal 1.618.

Worked example: split 100 units by the golden ratio 

• Larger portion = 100/1.618 = 61.8
• Smaller portion = 100 − 61.8 = 38.2 

Check both relationships.

• 100 ÷ 61.8 = 1.618  
• 61.8 ÷ 38.2 = 1.618 

That is the quality that makes it different. No other split point delivers both results. 

The fibonnaci link. The Fibonacci series is where you add every number to the previous one: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89. Divide any number by the previous number and you get closer to phi . 8 ÷ 5 = 1.60. 34 ÷ 21 = 1.619. 89 ÷ 55 = 1.6182. The farther you go the tighter it gets.

An honest word on the art charges. The “golden ratio” does show up in deliberate design work. It formed the basis of Le Corbusier’s Modulor system of proportioning. Many modern designers use it to set type scales, grid proportions and layout divisions, and it produces pleasing results.

There is greater doubt about the larger claims than is often acknowledged. The Parthenon, the Great Pyramid and the Mona Lisa are sometimes said to have been built using a golden ratio, although these readings are mainly retrofitted. If you make enough rectangles over any intricate artwork you get something close to 1.618. The builders or the painters did it there is no indication of that. Use phi because it provides you with a functional percentage system, not because of the mythology associated with it.

Waist and Height Ratio Calculator

Waist-to-height ratio, or WHtR, compares your waist measurement to your height. It offers an estimate of central adiposity (fat carried around the abdomen), which research shows is more closely related to health risk than overall body weight.

Waist-to-Height Ratio = Waist Circumference ÷ Height 

Both measurements must be in the same unit of measure. Inches with inches, centimeters with centimeters. The outcome is a decimal without a unit, which is why it works the same in every part of the world.

Worked example: 32-inch waist, 68-inch height

• 32 ÷ 68 = 0.47

How to measure your waist correctly with the help of ratio calculator Locate the gap between the bottom of your ribs and the top of your hip bone, typically right above your belly button. Wrap the tape there, keeping it level, and take the reading at the end of a typical exhalation. Don’t tighten it down, and don’t go by your pant size, which is sometimes a couple of inches off.

How the number is normally pronounced. NICE’s UK health guidance essentially classifies adults as 0.4 to 0.49 = no higher risk 0.5 to 0.59 = increased risk and 0.6 or above = further increased risk. Short version: Keep your waist less than half your height.

This is a population screening recommendation, not a diagnosis. It does not take into consideration your age, your muscle mass, your medical history, or anything else that is unique to you. If you have a number outside the first band, then that’s a reason to have a chat with a doctor. No more, no less. You may wish to see this in conjunction with additional measures that a healthcare professional can do.

Ratio Calculator FAQs

Q1. How do I simplify a ratio?

Find the largest common divisor of both numbers. Divide each side by it. The highest number that 24 and 36 can be divided by is 12 therefore 24 ÷ 12 = 2 and 36 ÷ 12 = 3, so you get 2:3. Three-part ratios are the same, but use the GCD of the three numbers.

Q2. What is a good aspect ratio for video?

16:9 is the modern standard for horizontal video and works on just about every TV, monitor and YouTube player. Use 9:16 for vertical content on TikTok, Reels and Shorts. 21:9 delivers a theatrical widescreen image using screen ratio calculator while 4:3 is largely history now, although it still appears in older archive video and some purposefully vintage cuts.

Q3. How do I calculate a gear ratio?

Divide the teeth on the driving gear by the teeth on the driven gear. A driven gear of 40 teeth and a driving gear of 10 teeth provides 40 ÷ 10 = 4, or 4:1. The driven gear turns one time for every four rotations of the driving gear which gives you about four times the torque at 1/4 the speed.

Q4. What is a good debt-to-income ratio?

The often mentioned comfort zone is around 36% or less. The 43% figure has long been the baseline for mortgages in the US, and many lenders may approve above this based on your credit score, savings and deposit. Thresholds vary by lender, loan product and country, so take any one number as a guide, not a cutoff.

Q5. What is the golden ratio used for?

Mostly design: putting up type scales, breaking up page layouts and proportioning grids. A good documented example in architecture is Le Corbusier’s Modulor system. Claims that ancient monuments and Renaissance paintings were built on it are usually post factum and rejected by historians. It is a proportion tool in its own right.

Q6. What waist-to-height ratio is considered healthy?

Many utilize the guideline of having your waist smaller than half your height which is below roughly 0.5. UK advice defines 0.4 to 0.49 as no increased risk, 0.5 to 0.59 as increased risk and 0.6 or higher as further increased risk. This is a generic screening instrument, not an individual diagnosis.

Conclusion

Five very distinct challenges, one common idea. You’re editing a movie, or picking a sprocket, or filling out a mortgage application or putting out a page, or checking a tape measure. You’re taking a pair of numbers and saying how they relate. The whole basis is the simplification method at the top of this page. Each use case adds one step on top of it.

You can run any of these without the arithmetic to use the tabs on the ratio calculator above. But the manual way is good to know, as it means you may sanity check a result anywhere, on paper, without a tool in front of you. If a number ever appears wrong run it through by hand and you will typically catch the mistake in under a minute.