Where this number comes from: Arithmetic: A4 is 210 × 297 mm. At 300 dots per inch that is 210 ÷ 25.4 × 300 ≈ 2480 and 297 ÷ 25.4 × 300 ≈ 3508 pixels.
There is no mystery in this number. A4 is 210 × 297 mm, an inch is 25.4 mm, and 300 dots per inch is the figure commercial printers ask for. Multiply it out and you get 2480 × 3508 pixels. At 150 DPI, which is enough for something viewed at arm's length, it is 1240 × 1754.
A caveat worth stating plainly: resizing an image up to 2480 × 3508 does not give it 300 DPI worth of detail. If the original is 800 px wide, enlarging it produces a file with the right pixel count and the same amount of real information, and it will print soft. Pixel dimensions are a container, not a quality. This tool fills the frame from what you give it and does not pretend otherwise.
This page sets pixel dimensions only. It does not write a DPI tag into the file, and for most print workflows that does not matter — a print shop asking for "A4 at 300 DPI" is asking for these pixel dimensions. If your printer specifically requires the metadata field set, that is a job for a layout or photo application, not a browser resizer.
Questions
What is A4 at 150 DPI?
1240 × 1754 pixels. Same arithmetic, half the resolution — fine for anything read at normal distance, and a quarter of the file size.
Does this set the DPI metadata in the file?
No. It sets the pixel dimensions, which is what a print shop means by "A4 at 300 DPI" in practice. The DPI tag itself is only a hint and most print workflows ignore it.
Can I get 300 DPI from a small image?
You can get the pixel count. You cannot get the detail — enlarging invents nothing. If the original is small, it will print soft no matter what number is in the file.
What about landscape A4?
Swap the numbers: 3508 × 2480. Set the width and height fields by hand, the tool takes any values.