The question sounds like it wants a calculator, and it does — but the whole calculator is one division. Inches = pixels ÷ DPI. Pick the density the job needs, divide each pixel dimension by it, and the print size falls out. Run it the other way — multiply inches by DPI — and you get the pixel count to export. Everything below is that formula pre-computed for the sizes people actually print.

Both directions of the same line

• Have pixels, want inches: a 6000×4000 file at 300 DPI prints 6000÷300 × 4000÷300 = 20 × 13.3 in. At 150 DPI the identical file goes 40 × 26.7 in.
• Have inches, want pixels: a 5×7 at 300 DPI needs 5×300 × 7×300 = 1500×2100 px — about 3.2 megapixels.
• Have both, want the verdict: a 2400×1800 file asked to cover 8×10 runs 240 DPI on the long edge and 225 on the short — the lower number, 225, is your real density.

The photo-size chart

Required pixels for common print sizes, at the two densities that cover almost every job:

Print size	Inches	@300 DPI (hand-held)	@150 DPI (wall / arm’s length)
4×6 photo	4×6	1200×1800 (2.2 MP)	600×900
5×7 photo	5×7	1500×2100 (3.2 MP)	750×1050
8×10 photo	8×10	2400×3000 (7.2 MP)	1200×1500
US Letter	8.5×11	2550×3300 (8.4 MP)	1275×1650
A4	8.27×11.69	2480×3508 (8.7 MP)	1240×1754
11×14	11×14	3300×4200 (13.9 MP)	1650×2100
A3	11.69×16.54	3508×4961 (17.4 MP)	1754×2480
12×18	12×18	3600×5400 (19.4 MP)	1800×2700
16×20	16×20	4800×6000 (28.8 MP)	2400×3000
20×30	20×30	6000×9000 (54 MP)	3000×4500
24×36 poster	24×36	7200×10800 (77.8 MP)	3600×5400 (19.4 MP)

The right-hand column is the sleeper: for anything that hangs on a wall, halving the density doubles the size you can cover — and nobody’s eye will catch it at a metre.

How big common sources actually print

Flip the lookup: take the resolution you have and divide by density. These are the largest clean prints each source makes — ÷300 for hand-held, ÷240 for the lab floor, ÷150 for the wall:

Source	Pixels	@300 DPI	@240 DPI	@150 DPI
Phone photo, 12 MP	4032×3024	13.4×10.1 in	16.8×12.6 in	26.9×20.2 in
Camera, 20 MP	5472×3648	18.2×12.2 in	22.8×15.2 in	36.5×24.3 in
Camera, 24 MP	6000×4000	20×13.3 in	25×16.7 in	40×26.7 in
Camera, 33 MP	7008×4672	23.4×15.6 in	29.2×19.5 in	46.7×31.1 in
Camera, 45 MP	8192×5464	27.3×18.2 in	34.1×22.8 in	54.6×36.4 in
Camera, 61 MP	9504×6336	31.7×21.1 in	39.6×26.4 in	63.4×42.2 in
4K video frame	3840×2160	12.8×7.2 in	16×9 in	25.6×14.4 in
1080p frame / screenshot	1920×1080	6.4×3.6 in	8×4.5 in	12.8×7.2 in
Square social post	1080×1080	3.6×3.6 in	4.5×4.5 in	7.2×7.2 in

Two things jump out. First, a 12 MP phone already covers every hand-held size through Letter and A4 — the megapixel race stopped mattering for prints long ago. Second, going from 300 to 150 DPI doubles the linear size you get for free; that’s not a compromise so much as a different product (wall art vs hand-held).

When 150 DPI is genuinely enough

Density requirements follow viewing distance, and anything meant for arm’s length or farther plays a different game:

• Wall prints and posters at ~1 m → 150 is indistinguishable from 300 at that range.
• Canvas wraps → the fabric texture consumes fine detail anyway; labs routinely accept 100–150.
• Photo books on a lap → 200–240 is a comfortable floor; 150 shows mild softness up close.
• Banners and trade-show graphics → 60–100; nobody inspects a banner with a loupe.

Hand-held sizes are the exception that built 300’s reputation — 4×6s, greeting cards, book pages held at 25 cm where the eye really can resolve the difference. Picking the number is a where-will-it-hang decision; the DPI guide goes deeper on that side.

When you’re short on pixels

Suppose the math lands at 170 DPI for the size you want. Three honest options, in order of preference:

1. Print smaller. A file with a 2048-pixel long edge covers 12 inches at ~170 DPI but 8 inches at 256 — inside the safe zone with zero resampling.
2. Accept the lower density. If it lives on a wall, 150–170 is fine and no one will ever know.
3. Upscale knowingly. A ≤2× resample of a clean file prints acceptably in most cases — but it invents pixels rather than recovering them, a budget you spend rather than detail you gain. Upscaling vs downscaling spells out the trade-offs.

What doesn’t help: editing the file’s “DPI” field. That number is a label — 2400 pixels is 2400 pixels whether the tag reads 72 or 600, and the pixel-size math explains why.

If the destination is a feed rather than paper, none of this applies — screens deal in pure pixel counts, which is what the social sizes table and the scaler are for.

The short version: divide each pixel dimension by your target DPI and the inches that come out are the truth — everything else is negotiation.

Frequently asked questions

How many pixels do I need for a 4×6 print?

1200×1800 px (about 2.2 megapixels) at the standard 300 DPI. At a still-decent 240 DPI: 960×1440. Even a modern mid-range phone clears the 300-DPI bar several times over.

Can a 1920×1080 image print an 8×10?

Not cleanly — it works out to ~140–190 DPI depending on the edge, which looks soft at reading distance. At 4×6 the same file delivers ~270–320 DPI, so it's fine for small prints. For the 8×10 you'd need to accept a wall-print density or upscale; the trade-offs are in upscaling vs downscaling.

Is A4 bigger than US Letter?

Taller but narrower: A4 is 210×297 mm (8.27×11.69 in); Letter is 8.5×11 in. At 300 DPI that's 2480×3508 px vs 2550×3300 px. Sending a Letter-proportioned file to an A4 frame means cropping or bars — the same fit problem as on screens.

What's the biggest print a 12 MP phone photo can make?

A 4032×3024 file prints 13.4×10.1 in at 300 DPI — comfortably past Letter/A4 — and stretches to roughly 27×20 in at the 150-DPI wall-print density. Megapixel count stopped being the print bottleneck years ago; what matters is matching density to viewing distance.

What DPI should I use for a poster people view from a distance?

150 DPI for anything seen from about a metre; 60–100 DPI for across-the-room graphics; 10–30 for billboards. The eye resolves angle, not absolute size — a poster at 150 viewed from a metre looks exactly as sharp as a 4×6 at 300 held in the hand.