DPI / PPI Calculator

A DPI/PPI calculator answers three related questions about the relationship between pixels and physical size. PPI (pixels per inch) describes how many physical pixels a screen packs into each inch, higher PPI means sharper text and graphics at a typical viewing distance. DPI (dots per inch) describes how many ink dots a printer lays down per inch, higher DPI captures finer detail. The two terms are often used interchangeably in casual speech, but they describe different things, and the calculator makes that distinction explicit. This page covers three sub-calculations: pixel density from a screen's resolution and diagonal, print size from a pixel count and a target DPI, and the pixel dimensions required for a target print size at a given DPI. A reference table of common print DPI targets and screen presets anchors sanity checks.

How to Use the DPI/PPI Calculator

1. Compute screen pixel density (PPI). Type the screen's native width in pixels, height in pixels, and the diagonal in inches. The result panel shows the diagonal in pixels, the PPI, the physical size of one pixel (pixel pitch), and the aspect ratio.
2. Compute print size from pixels and a target DPI. Type the pixel count (raw pixels or megapixels) and the target DPI. The result shows the print's size in inches and centimetres.
3. Compute required pixels for a target print size and DPI. Type the desired print width and height (inches or centimetres) and the target DPI. The result shows the pixel dimensions needed, the total pixel count, and the equivalent in megapixels.
4. Use the reference tables. The two tables at the bottom are general guidance: the first maps common DPI values to typical print use, and the second lists screen presets that load into the PPI calculator with one click.
5. Treat every reference value as a guideline. The table values are industry conventions, not vendor specifications.

The Formulas

Pixel density from resolution and diagonal. A rectangular display with width w pixels, height h pixels, and a diagonal measured in inches has a diagonal in pixels given by the Pythagorean theorem; the pixel density is the diagonal in pixels divided by the diagonal in inches:

diagonal_px = sqrt(w² + h²)
PPI         = diagonal_px / diagonal_in

This is the standard definition used by every display manufacturer. The same computation works for any rectangular image, not just screens.

Print size from pixels and DPI. A print at a given DPI has each linear inch of paper occupied by DPI image pixels. The physical size is:

print_in = pixels / DPI
print_cm = print_in × 2.54

The factor 2.54 cm per inch is exact (international yard and pound agreement, 1959). The converse, required pixels for a target print size, is the same equation inverted:

required_px = inches × DPI

Pixel pitch. On a screen with PPI p, each pixel occupies 25.4 / p millimetres. Below ~0.2 mm, individual pixels become invisible at a normal reading distance; above ~0.3 mm, text starts to look "pixelly" to users with good vision.

Worked Examples

Example 1, 1920×1080 on a 24-inch monitor. sqrt(1920² + 1080²) = sqrt(4 852 800) ≈ 2202.91 px. PPI = 2202.91 / 24 ≈ 91.79 PPI. The familiar "Full HD on 24-inch" result, slightly pixelly for text at native resolution, but adequate for general use.

Example 2, 2560×1440 on a 27-inch monitor. sqrt(2560² + 1440²) = sqrt(8 627 200) ≈ 2937.20 px. PPI = 2937.20 / 27 ≈ 108.79 PPI. QHD on 27", text is noticeably sharper than 91 PPI, and most users consider this the threshold for "retina-quality" desktop text at a typical viewing distance.

Example 3, 3000 pixels at 300 DPI. 3000 / 300 = 10 in. In centimetres: 10 × 2.54 = 25.4 cm. This is the standard "3000 pixels on the long edge" guideline that camera manufacturers often quote for "good 10-inch prints."

Example 4, 8×10 inch at 300 DPI. 8 × 300 = 2400 px on the short edge, 10 × 300 = 3000 px on the long edge. Total = 2400 × 3000 = 7.2 megapixels. The same 8×10 at 150 DPI needs only 1200×1500 = 1.8 megapixels, a four-fold reduction and a visible drop in print quality, but acceptable for drafts.

Example 5, 1920×1080 on a 15.6-inch laptop. Diagonal in pixels is the same ~2202.91 px. PPI = 2202.91 / 15.6 ≈ 141.21 PPI. Most "1080p laptop" spec sheets implicitly describe this value, far sharper than the 24-inch desktop at the same resolution because the pixels are packed into a much smaller diagonal.

Where It Shows Up

Buying a monitor or TV. Manufacturers quote a screen's diagonal in inches and its native resolution in pixels. Computing the PPI tells you whether the screen will look sharp at your viewing distance. Values above ~100 PPI are "retina-class" for desktop use; below ~80 PPI, individual pixels become visible at a normal reading distance.

Preparing an image for print. Print shops and image-editing software ask for a target DPI. For a "good" photo print, 300 DPI is standard; for a draft or screen preview, 150 DPI is often acceptable; for a large poster viewed from a distance, even 72 DPI may suffice.

Camera and scanner specifications. Cameras are marketed by megapixel count; scanners and printers by DPI. A 12 MP image produces a high-quality 8×10 print at 300 DPI (which needs 7.2 MP), with megapixels to spare for cropping.

Web design and CSS. CSS px units are not the same as physical pixels, they are reference pixels calibrated to a 96 DPI viewing convention. The calculator is useful for sanity-checking physical dimensions against CSS values, but the two systems are not directly equivalent at the code level.

Common Mistakes

Confusing DPI and PPI. DPI describes printer dots per inch; PPI describes screen pixels per inch. The numbers are not interchangeable, a "300 DPI" print contains 300 ink dots per inch, while a "300 PPI" screen has 300 pixels per inch. The underlying technology differs; using the terms interchangeably is the most common source of confusion in the topic.

Confusing screen inches with marketing inches. A "24-inch" monitor typically has a visible diagonal of about 23.5 to 24.0 inches depending on bezel and chassis design. The number on the box is rounded; use the published visible-diagonal spec from the manufacturer. Small errors in the diagonal propagate roughly linearly into the PPI.

Quoting DPI without a print size. "300 DPI" by itself is meaningless. A 300 DPI image that is 1×1 inch has 300×300 = 90,000 pixels; the same 300 DPI image at 12×18 inches has 3600×5400 = 19.4 megapixels. Always specify DPI together with the physical print size.

Forgetting to scale before interpolating. Image-editing software can resample a small image to a larger pixel count, but the new pixels are interpolated, not captured. Resampling 2 MP to 12 MP at 300 DPI does not give "12 MP of detail", it gives 2 MP of actual detail spread over 12 MP of canvas. Start with a pixel count that matches the target DPI and physical size.

Treating higher DPI as always better. Beyond a viewing-distance-dependent threshold, additional DPI is wasted. A 600 DPI print viewed from 30 cm is indistinguishable from a 300 DPI print for most viewers with normal vision. Higher DPI helps when the print is viewed up close (gallery prints, fine art) or when the medium can resolve it.

Using the wrong DPI for the output medium. Photo paper, plain paper, canvas, and fabric all have different optimum DPI bands. A quick sanity check: 300 DPI for photo paper, 150 DPI for draft plain paper, 72 DPI for screen preview, 600+ DPI for fine-art reproduction. The exact optimum depends on the printer, paper, and viewing distance.

Reference: Print DPI Targets

The table below maps common DPI values to typical print uses. These are general industry conventions, not vendor specifications, exact optimum DPI depends on the printer driver, the paper, and the viewing distance.

Reference: Screen Presets

The screen presets below are common resolution-and-diagonal pairs. Click a preset to load its width, height, and diagonal into the PPI calculator. These are illustrative common values; actual marketed displays vary.

For any given diagonal, halving the pixel pitch (doubling the PPI) roughly quadruples the total pixel count. Going from 24-inch 1080p to 24-inch 4K is not "twice as sharp", it is four times as sharp, because both dimensions double.

Frequently Asked Questions

What is the difference between DPI and PPI?

DPI (dots per inch) counts ink dots a printer lays down per inch of paper. PPI (pixels per inch) counts the physical pixels a screen displays per inch of glass. The two describe different technologies but the same underlying ratio, pixels (or dots) per linear inch, and the math for converting a pixel count to a physical size is the same. In casual usage the terms are swapped, but the calculator uses PPI for screens and DPI for print to make the distinction explicit.

What PPI do I need for a "retina" display?

There is no single threshold, "retina" is a marketing term, not a specification. Apple originally defined it as the PPI at which a user with 20/20 vision cannot distinguish individual pixels at a typical viewing distance. For a desktop monitor viewed from ~60 cm, that works out to roughly 200 PPI; for a phone held ~25 cm away, the threshold is closer to 400 PPI. As a rule of thumb, above ~100 PPI on a desktop is acceptable for text work, and above ~150 PPI is "very sharp."

How many DPI do I need to print a good photo?

300 DPI is the standard target for photo-quality prints at typical viewing distances. 150 DPI is acceptable for draft prints and large-format prints viewed from a distance. 600 DPI is useful for fine-art reproduction and gallery prints viewed up close. Below 150 DPI the print looks visibly soft at close range; above 600 DPI the additional detail is generally indistinguishable to the eye on most paper stocks.

My monitor is advertised as "27-inch" but the PPI calculator gives a different number. Why?

The advertised diagonal is usually rounded to the nearest inch or half-inch. The actual diagonal of the visible image area depends on the bezel design, the chassis, and the panel itself. If you have access to the manufacturer's spec sheet, the published "viewable image area" diagonal is the number to use. A 0.5-inch error in the diagonal propagates roughly linearly into the PPI.

Can I convert a pixel count to a print size without knowing the DPI?

No. The print size depends on the DPI you choose. The same 12-megapixel image can be printed at 4×6 inches at 600 DPI, 8×10 inches at 300 DPI, or 16×20 inches at 150 DPI. The pixel count is fixed; the print size depends on the DPI you select. The calculator's second sub-calculator resolves this by letting you specify both the pixel count and the DPI.

Why do my scans at 600 DPI look no better than scans at 300 DPI?

Two reasons. First, the scanned medium may not contain detail finer than 300 DPI can capture, a 35 mm slide, for example, has a finite resolution limit. Second, the scanner's optical resolution may be lower than its advertised (interpolated) resolution. Optical DPI is the meaningful number; interpolated DPI is the scanner's software filling in extra pixels between the optical samples. For sharp scans, look at the optical DPI in the spec sheet.

What is the relationship between megapixels and print size?

Megapixels = (width × height) / 1,000,000. A 12 MP image is roughly 4000×3000 pixels. At 300 DPI that gives a print of about 13.3×10 inches, a generous 8R or A4 with room to spare. At 150 DPI, the same 12 MP image prints at 26.7×20 inches, a large poster, but visibly soft at close range. The calculator's third sub-calculator gives the exact pixel dimensions needed for any target print size and DPI.

Is higher DPI always better on a screen?

Not always. Above the eye's resolution limit at the viewing distance, additional PPI is wasted. The waste is small at the panel level (a 600 PPI phone display uses marginally more power than a 400 PPI one), but manufacturers sometimes advertise extreme PPI values that exceed what the eye can resolve at normal viewing distances. A 4K 27-inch monitor (~163 PPI) is at the high end of useful; beyond ~250 PPI on a desktop, the benefit is marginal for users with normal vision.

Can I use this calculator for vinyl cutting, embroidery, or other craft applications?

Yes. The math is the same, pixels/dots per inch and physical dimensions work for any medium where you have a discrete unit of resolution to map onto a continuous physical dimension. Vinyl cutters and embroidery machines are usually specified in DPI or "stitches per inch." Enter the pixel count and the machine's DPI to get the physical size, or enter the physical size and the DPI to get the required pixel count.

References

• NIST, 1 inch = 2.54 cm exactly. The international yard and pound agreement of 1959 defines the inch as exactly 25.4 millimetres. This conversion factor underlies every print and screen size calculation.
• Wikipedia, "Pixel density" and "Dots per inch". Standard overview of how PPI and DPI are defined and applied across screens and printers. The diagonal-decomposition formula PPI = sqrt(w² + h²) / d_in is the canonical definition.
• ISO 12647, Graphic technology, Process control for the production of half-tone colour separations, proof and production prints. International standard for print quality control. It specifies the screening, colour, and resolution conventions used in commercial printing; the 300 DPI target for photo prints is an industry convention informed by this standard.
• Adobe / GIMP / Photoshop print guidelines. Documented recommendations for "draft / good / best" print DPI bands. Adobe's print dialog defaults to 300 DPI for photo-quality output; GIMP and Photoshop let the user override. General guidelines, not vendor specifications.
• General industry conventions for print DPI targets. The 72 / 150 / 300 / 600 DPI bands are conservative reference values based on viewing distance, paper type, and typical print-shop expectations. They are not vendor specifications and may need adjustment for specific use cases.