For those who worry about such things, the Pixels Per Inch is shown in the third column.  Obviously, the greater the PPI, the better the image quality. It's generally not recommended to print at less than 96 PPI, but it's your choice.

The chart below shows the LARGEST image you can get that is properly proportioned for various print sizes with a lengthwise crop or crosswise crop.  If you want to crop a smaller area, it should be proportional to the crop dimensions shown, and the PPI will be reduced accordingly.

Original image: 480 x 640 pixels

	Lengthwise Crop		Crosswise Crop
To print this size (inches)	Crop original to this size (pixels)	PPI	Crop original to this size (pixels)	PPI
3.5 x 5	448 x 640	128	480 x 336	96
4 x 6	424 x 636	106	480 x 320	80
5 x 7	455 x 637	91	476 x 340	68
8 x 10	480 x 600	60	480 x 384	48
8.5 x 11	476 x 616	56	473 x 365	43
11 x 14	473 x 602	43	476 x 374	34
16 x 20	480 x 600	30	480 x 384	24

 

Original image: 768 x 1024 pixels

	Lengthwise Crop		Crosswise Crop
To print this size (inches)	Crop original to this size (pixels)	PPI	Crop original to this size (pixels)	PPI
3.5 x 5	714 x 1020	204	765 x 535	153
4 x 6	680 x 1020	170	768 x 512	128
5 x 7	730 x  1022	146	763 x 545	109
8 x 10	768 x 960	96	760 x 608	76
8.5 x 11	765 x 990	90	759 x 586	69
11 x 14	759 x  966	69	756 x 594	54
16 x 20	768 x 960	48	760 x 608	38

 

Original image: 912 x 1216  pixels

	Lengthwise Crop		Crosswise Crop
To print this size (inches)	Crop original to this size (pixels)	PPI	Crop original to this size (pixels)	PPI
3.5 x 5	850 x 1215	243	910 x 637	182
4 x 6	808 x 1212	202	912 x 608	152
5 x 7	865 x  1211	173	910 x 650	130
8 x 10	912 x 1140	114	910 x 728	91
8.5 x 11	909 x 1177	107	902 x 697	82
11 x 14	902 x  1148	82	910 x 715	65
16 x 20	912 x 1140	57	900 x 720	45

 

Original image: 960 x 1280 pixels

	Lengthwise Crop		Crosswise Crop
To print this size (inches)	Crop original to this size (pixels)	PPI	Crop original to this size (pixels)	PPI
3.5 x 5	896 x 1280	256	960 x 672	192
4 x 6	852 x 1278	213	960 x 640	160
5 x 7	910 x 1274	182	959 x 685	137
8 x 10	960 x 1200	120	960 x 768	96
8.5 x 11	952 x 1232	112	957 x 739	87
11 x 14	957 x  1218	87	952 x 748	68
16 x 20	960 x 1200	60	960 x 768	48

 

Original image: 1104 x 1472  pixels

	Lengthwise Crop		Crosswise Crop
To print this size (inches)	Crop original to this size (pixels)	PPI	Crop original to this size (pixels)	PPI
3.5 x 5	1029 x 1470	294	1100 x 770	220
4 x 6	980 x 1470	245	1104 x 736	184
5 x 7	1050 x 1470	210	1099 x 785	157
8 x 10	1104 x 1380	138	1100 x 880	110
8.5 x 11	1096 x 1419	129	1100 x 850	100
11 x 14	1100 x 1400	100	1092 x 858	78
16 x 20	1104 x 1380	69	1100 x 880	55

 

Original image: 1066 x 1600 pixels

	Lengthwise Crop		Crosswise Crop
To print this size (inches)	Crop original to this size (pixels)	PPI	Crop original to this size (pixels)	PPI
3.5 x 5	1064 x 1520	304	1065 x 745	213
4 x 6	1064 x 1596	266	1062 x 708	177
5 x 7	1065 x 1491	213	1064 x 760	152
8 x 10	1064 x 1330	133	1060 x 848	106
8.5 x 11	1062 x 1375	125	1056 x 816	96
11 x 14	1056 x 1344	96	1064 x 836	76
16 x 20	1056 x 1320	66	1060 x 848	53

 

Original image: 1200 x 1600 pixels

	Lengthwise Crop		Crosswise Crop
To print this size (inches)	Crop original to this size (pixels)	PPI	Crop original to this size (pixels)	PPI
3.5 x 5	1120 x 1600	320	1200 x 840	240
4 x 6	1064 x 1596	266	1200 x 800	200
5 x 7	1140 x 1596	228	1197 x 855	171
8 x 10	1200 x 1500	150	1200 x 960	120
8.5 x 11	1198 x 1551	141	1199 x 926	109
11 x 14	1199 x  1526	109	1190 x 935	85
16 x 20	1200 x 1500	75	1200 x 960	60

Why bother with custom cropping for prints?

     Most home printing software will leave a white border if your original file is not in the correct proportions for the
     print size you have selected.

     If you send a photo to an online printing service, and you don't crop the file to the correct proportions for the print
     size you have selected, then either you will get a print with white borders or you will get a borderless print that has
     been cropped arbitrarily. A few pixels here and there might not make much of a difference in a landscape or in a
     photo whose subject is at the centre.

     But if any part of your subject is near the borders of your image, you don't know what you will get if you leave
     automatic cropping to the photofinisher. For example, in the photo below, the clown's entire balloon hat is visible
     in MY crop (on the left), but it is lopped off in the centred crop (on the right), which is typical of what most
     photofinishers would do.

     (The original image was 480 x 640.  For the correct proportions for a 5 x 7 inch print, cropped size is 637 x 455. I
     reduced the images to half size for web display.)

     I provided the cropping chart above for those who prefer to have control of the cropping process instead of leaving it to
     the photofinisher. (You don't HAVE to do this if you don't mind letting the photofinisher crop automatically.)

How to do custom cropping in Ulead PhotoImpact 4.2:
[Most graphics software will allow you to do something similar.]

Step 1
Open the original photo file, let's say original.jpg.
CTRL-D to duplicate it. (Always work on a copy.)

Step 2
Check the dimensions of your original photo (Width and Height in pixels is displayed above the photo, or you can click View - Photo Properties). Decide what size print you want to make, let's say 5x7 inches, and select the cropping size from the chart on this webpage.

Step 3
Use the SELECTION TOOL, New, Rectangle. Checkmark Fixed Size and enter the desired Width and Height from the chart on this webpage.  Click on the image. If the selection is not where you want it, click on Options - Move Selection Marquee and drag the selection rectangle wherever you want it. Make sure the entire selection rectangle is visible.

Step 4
CTRL-R to crop the image.
File - Save As ... with a new name, let's say cropped-5x7.jpg
That's the file to use for printing.

How to do your own calculations for other print sizes to preserve maximum pixels from the original photo:

For this calculation, we will refer to the greater dimension as width.  For example, if the original image is 1200x1600, we will say [width of original in pixels] = 1600, regardless of the orientation of the image.  Similarly, we will call the greater dimension of the print [width of print in inches].

PPI = Integer part of ([width of original in pixels]/[(width of print in inches])
Crop Width = PPI x [width of print in inches]
Crop Height = PPI x [height of print in inches]

If this yields a Crop Height  greater than the [height of original in pixels] or Crop Width greater than the [width of original in pixels], then redo the calculation:

PPI = Integer part of ([height of original in pixels]/[(height of print in inches])
Crop Width = PPI x [width of print in inches]
Crop Height = PPI x [height of print in inches]

Example1:
Original 480 x 640 pixels. Print 3.5 x 5 inches:

640/5 = 128, PPI = 128
128 x 3.5 = 448
128 x 5 = 640
Crop to 448 x 640 pixels.

Example2:
Original 1200 x 1600 pixels. Print 8.5 x 11 inches:

1600/11 = 145.4545, PPI = 145
145 x 8.5 = 1232.5
145 x 11 =  1595
Crop to 1232 x 1595 pixels. <== NO GOOD. Height greater than 1200, so redo calculation of PPI for the other dimension.

1200/8.5 = 141.176, PPI = 141
141 x 8.5 = 1198.5
141 x 11 = 1551
Crop to 1198 x 1551 pixels

It is certainly possible to crop to smaller sizes, proportionally, but the smaller the cropped area, the more detail will be lost in the print.