Aspect Ratio Calculator

Enter a width and a height in pixels and the calculator reduces them to the simplest ratio describing their shape, such as 16:9 for 1920 by 1080. It also reports the decimal form, width divided by height, and whether the frame is landscape, portrait or square. Switch to the second mode and, given the original dimensions and a new width, it returns the matching height that keeps the proportions intact.

How the reduction works

An aspect ratio is a fraction wearing a colon, so simplifying one is the familiar business of cancelling a fraction to lowest terms. The calculator finds the greatest common divisor of the width and the height, the largest whole number that divides both exactly, and divides each side by it.

ratio = w ÷ gcd(w, h) : h ÷ gcd(w, h)

The divisor comes from the remainder method: divide the larger number by the smaller, keep the remainder, and repeat with the smaller number and that remainder until nothing is left; the last divisor used is the greatest common divisor. The procedure is the Euclidean algorithm, set out in Propositions 1 and 2 of Book 7 of Euclid's Elements around 300 BC and still among the oldest algorithms in routine use. Beyond the reduced pair, the calculator reports the same shape as a single number,

decimal = w ÷ h

and, in the resize mode, the height that preserves the shape at a new width:

new height = round(new width × h ÷ w)

A presentational rule sits on top: when either side of the reduced ratio lands above 50, the exact fraction is correct but unreadable, so the calculator prints the shape against a height of 1 instead, such as 1.78:1, rounded to two places. The threshold is strict: a reduced term of exactly 50 still prints as a fraction and only 51 or more triggers the switch, so 50:1 stays as written while 51:1 becomes 51.00:1.

Three worked examples

Start with the defaults, 1920 by 1080. The remainder method: 1920 divided by 1080 leaves 840, then 1080 divided by 840 leaves 240, then 840 divided by 240 leaves 120, and 240 divided by 120 leaves nothing. The greatest common divisor is 120, so the sides reduce to 1920 ÷ 120 = 16 and 1080 ÷ 120 = 9, the familiar 16:9, and the decimal form is 1920 ÷ 1080 = 1.7778.

Now try 1366 by 768. The only common divisor is 2, so the reduced ratio is 683:384 — exact and unreadable. Because 683 is far past 50, the calculator prints the decimal convention instead: 1366 ÷ 768 = 1.7786, displayed as 1.78:1, a whisker wider than 16:9.

For the resize mode, keep 1920 by 1080 and ask for a new width of 1280. The matching height is 1280 × 1080 ÷ 1920 = 720 exactly, so 1280 by 720 has precisely the original shape; ask for 7680 instead and the same arithmetic returns 4320, the 8K UHD frame. The division does not always land so neatly: scale 1366 by 768 to a width of 1000 and the raw answer is 562.2255, which the calculator rounds to 562, since screens have no fractional pixels.

From Edison's workshop to the Academy ratio

The 4:3 shape that governed the first century of the moving image was fixed in 1892 in Thomas Edison's laboratory, where W. K. L. Dickson, building the Kinetoscope, settled on 35 mm film with a frame four perforations high, an image four units wide for every three high. Everything built to shoot or show that stock inherited the shape. Sound disturbed it: the optical soundtrack added in the late 1920s ran down one edge and cut into the picture, so in 1932 the Academy of Motion Picture Arts and Sciences standardised a rebalanced frame of 1.375:1, since known as the Academy ratio, after similar sizes had been in use as early as 1928. On May 9, 1932 the SMPE matched it with a projector aperture of 0.825 by 0.600 inches, a pair whose quotient is exactly 1.375 and which reduces to 11:8. The Academy ratio is not 4:3: at 1.375 it is a shade wider than the 1.3333 silent frame. Virtually every 35 mm studio film from 1932 to 1952 was shot in it.

The 1950s broke the settlement. Television, which had copied cinema's near-4:3 frame, reached the living room, and the studios' answer was width. Cinerama's three-projector spectacle This Is Cinerama opened at the Broadway Theatre in New York on September 30, 1952, The Robe premiered on September 16, 1953 as the first film released in CinemaScope, and the format war that followed produced ratios as wide as 2.6:1 from CinemaScope, 2.20:1 from Todd-AO and 2.00:1 from VistaVision. The industry eventually consolidated on the two frames that still dominate features, 1.85:1 and 2.39:1, the wider figure nudged from 2.35:1 by a 1970 SMPTE aperture revision, PH22.106-1971, meant to make splices less visible, though the 2.35 shorthand survives in casual speech.

Digital cinema kept exactly those two. SMPTE ST 428-1 defines a 4K Flat container of 3996 by 2160 pixels and a Scope container of 4096 by 1716, and both behave honestly here: the first reduces to 37:20, which is 1.85 exactly, while the second reduces to 1024:429 and so prints as 2.39:1.

The overlay that produced 16:9

The modern screen shape was built as a compromise between every older format. In 1984, within the SMPTE Working Group on High-Definition Electronic Production, the engineer Kerns H. Powers took the aspect ratios then in active use, from 4:3 to the widest cinema formats, drew each one as a rectangle of equal area, and stacked the rectangles on a common centre. Two shapes fell out of the pile: the smallest rectangle that enclosed every format, and the largest rectangle that fitted inside every one. Their proportions are necessarily the same, and equal to the geometric mean of the narrowest and widest ratios in the set, which places the target between roughly 1.77 and 1.79 depending on where the wide end is drawn. The nearest shape in small whole numbers, 16:9 at 1.7778, is what the standards bodies wrote down, and it became the international format for high-definition television. The European Union backed it with a 16:9 Action Plan from 1993, and since 1999 it has been the most common ratio for televisions.

A tidier story circulates alongside the real one: that 16:9 is the geometric mean of the narrowest and widest formats of the day. The arithmetic refuses to cooperate. Multiply 4 ÷ 3 by 2.39 and take the square root and the result is about 1.785; against the older 2.35 figure it is about 1.770, and against 2.40 about 1.789. None of them equals 16 ÷ 9, which is 1.7778. The near miss has a cause: the overlay does land on that mean by construction, but the mean is where the method pointed, not where the standard settled.

Why cinema quotes decimals

Film ratios rarely reduce to small whole numbers, so the industry normalises the height to 1 and quotes the width as a decimal. The virtue is instant comparison: no arithmetic is needed to see that 2.39:1 is wider than 1.85:1. This calculator borrows the convention for unwieldy pairs.

Marketing labels repay the same scrutiny. Monitors sold as 21:9, a marketing term Philips first used in January 2009, rarely reduce to it: a 3440 by 1440 panel comes out as 43:18, about 2.389, and the 2560 by 1080 variant reduces to 64:27, which the threshold rule prints here as 2.37:1. Both sit deliberately close to cinema's 2.39:1 Scope frame; a true 21:9 would be a narrower 2.33.

Phones are mostly held upright, so the 16:9 rectangle now spends much of its life on its side: vertical video, popularised by Snapchat and Instagram, is framed at 9:16, the same shape rotated a quarter turn, and TikTok, Instagram Reels and YouTube Shorts all treat 1080 by 1920 pixels as its native full-screen delivery, a pair that reduces to 9:16 exactly. Entered that way round, the calculator returns 9:16, a decimal of 0.5625 and a portrait orientation, and scaling a 9:16 frame to 1080 wide in resize mode hands back 1920. A portrait result is therefore often the intended shape rather than a mistake.

Assumptions and edge cases

Width, height and new width must be whole numbers of pixels from 1 to 100,000; anything outside that is refused with a message rather than rounded or clipped. The decimal output is computed at full precision and rounded to four places for display. In resize mode the matching height is rounded to the nearest whole pixel, so a scaled frame can sit a hair off the true shape. The reduced ratio, decimal and orientation always describe the original width and height you entered, not the resized frame. Orientation uses strict comparisons: wider than tall is landscape, taller than wide is portrait, and only exactly equal sides count as square.

Frequently asked questions

What aspect ratio is 1920x1080?

16:9. The largest number that divides both 1920 and 1080 exactly is 120, and dividing each side by it leaves 16 and 9. As a decimal that is 1920 ÷ 1080 = 1.7778, and since the width exceeds the height the orientation is landscape. Any resolution whose sides reduce to the same pair, such as 1280 by 720 or 3840 by 2160, has the identical shape.

How do you simplify an aspect ratio by hand?

Find the greatest common divisor of the width and height, then divide both by it. The quick route is the remainder method: divide the larger number by the smaller and keep the remainder, then repeat with the smaller number and that remainder until nothing is left. For 1920 and 1080 the remainders run 840, 240, 120 and then 0, so the divisor is 120 and the ratio reduces to 16:9.

Why do movies use ratios like 1.85:1 and 2.39:1 instead of whole numbers?

Cinema normalises the height to 1 and quotes the width as a decimal, because film ratios rarely reduce to small whole numbers and decimals compare at a glance: 2.39 is plainly wider than 1.85. Most modern features use one of those two ratios. This calculator adopts the same convention whenever a reduced term passes 50, which is why 1366 by 768 appears as 1.78:1 rather than the exact but unreadable 683:384.

How do I resize an image without stretching it?

Multiply the new width by the original height, divide by the original width, and round to the nearest whole pixel. Scaling a 1920 by 1080 frame to 1280 wide gives 1280 × 1080 ÷ 1920 = 720, so the resized frame is 1280 by 720. Set the calculator to the missing-height mode and it performs exactly this arithmetic for any dimensions.

Where does the 16:9 widescreen ratio come from?

From a comparison run in 1984 by the engineer Kerns H. Powers within the SMPTE Working Group on High-Definition Electronic Production. He drew the aspect ratios then in use as rectangles of equal area stacked on a common centre, and found that the smallest rectangle enclosing all of them and the largest rectangle fitting inside all of them share the same shape, the geometric mean of the extreme ratios in the set, near 1.77 to 1. The nearest ratio in small whole numbers, 16:9 at 1.7778, is the one the standards bodies took up, and since 1999 it has been the most common television ratio.

Is 16:9 the geometric mean of 4:3 and widescreen cinema?

No, although the claim is widely repeated. The geometric mean of 4 ÷ 3 and 2.39 is the square root of their product, about 1.785, and against the older 2.35 figure it is about 1.770. Neither equals 16 ÷ 9, which is 1.7778. The near miss has a cause: an overlay of equal-area rectangles lands on the geometric mean of the extremes by construction, so Kerns Powers's rectangles pointed somewhere in the 1.77 to 1.79 band, and 16:9 happened to be the nearby ratio in small whole numbers that was adopted.