[c#] Convert Pixels to Points

I have a need to convert Pixels to Points in C#. I've seen some complicated explanations about the topic, but can't seem to locate a simple formula. Let's assume a standard 96dpi, how do I calulate this conversion?

Actually it must be

points = pixels * 96 / 72

Height lines converted into points and pixel (my own formula). Here is an example with a manual entry of 213.67 points in the Row Height field:

213.67  Manual Entry    
  0.45  Add 0.45    
214.12  Subtotal    
213.75  Round to a multiple of 0.75 
213.00  Subtract 0.75 provides manual entry converted by Excel  
284.00  Divide by 0.75 gives the number of pixels of height

Here the manual entry of 213.67 points gives 284 pixels.
Here the manual entry of 213.68 points gives 285 pixels.

(Why 0.45? I do not know but it works.)

Assuming 96dpi is a huge mistake. Even if the assumption is right, there's also an option to scale fonts. So a font set for 10pts may actually be shown as if it's 12.5pt (125%).

points = (pixels / 96) * 72 on a standard XP/Vista/7 machine (factory defaults)

points = (pixels / 72) * 72 on a standard Mac running OSX (Factory defaults)

Windows runs as default at 96dpi (display) Macs run as default at 72 dpi (display)

72 POSTSCRIPT Points = 1 inch 12 POSTSCRIPT Points = 1 POSTSCRIPT Pica 6 POSTSCRIPT Picas = 72 Points = 1 inch

1 point = 1/72 inches = 25.4/72 mm = 0.3527 mm

DPI = Dots Per Inch PPI = Pixels Per Inch LPI = Lines per inch

More info if using em as measuring

16px = 1em (default for normal text) 8em = 16px * 8 Pixels/16 = em

This works:

int pixels = (int)((dp) * Resources.System.DisplayMetrics.Density + 0.5f);

WPF converts points to pixels with the System.Windows.FontSizeConverter. The FontSizeConverter uses the System.Windows.LengthConverter. The LengthConverter uses the factor 1.333333333333333333 to convert from points (p) to pixels (x): x = p * 1.3333333333333333

Starting with the given:

• There are 72 points in an inch (that is what a point is, 1/72 of an inch)
• on a system set for 150dpi, there are 150 pixels per inch.
• 1 in = 72pt = 150px (for 150dpi setting)

If you want to find points (pt) based on pixels (px):

 72 pt    x pt
------ = -----                  (1) for 150dpi system
150 px    y px

Rearranging:

x = (y/150) * 72                (2) for 150dpi system

so:

points = (pixels / 150) * 72    (3) for 150dpi system

Try this if your code lies in a form:

Graphics g = this.CreateGraphics();
points = pixels * 72 / g.DpiX;
g.Dispose();

Using wxPython on Mac to get the correct DPI as follows:

    from wx import ScreenDC
    from wx import Size

    size: Size = ScreenDC().GetPPI()
    print(f'x-DPI: {size.GetWidth()} y-DPI: {size.GetHeight()}')

This yields:

x-DPI: 72 y-DPI: 72

Thus, the formula is:

points: int = (pixelNumber * 72) // 72

Surely this whole question should be:

"How do I obtain the horizontal and vertical PPI (Pixels Per Inch) of the monitor?"

There are 72 points in an inch (by definition, a "point" is defined as 1/72nd of an inch, likewise a "pica" is defined as 1/72nd of a foot). With these two bits of information you can convert from px to pt and back very easily.

System.Drawing.Graphics has DpiX and DpiY properties. DpiX is pixels per inch horizontally. DpiY is pixels per inch vertically. Use those to convert from points (72 points per inch) to pixels.

Ex: 14 horizontal points = (14 * DpiX) / 72 pixels