Metrically compatible fonts
In this page, I will show you fonts with characters that are the same width as other well-known fonts. All of the fonts on this list are released under an open source license, allowing for unrestricted use, sharing, and modification. It is recommended that you check each font's license before downloading it.
Metrical compatibility means that if you start writing a text in Helvetica and then switch to Arial, the text's proportions will not change. Both Helvetica and Arial are proprietary fonts, which means that you have more restrictions and must pay a license to use them in a specific way. Free fonts allow you to have more control over them without having to pay a license fee.
Below are the names of some popular Windows fonts; clicking on them will take you to another page if there are more than one alternative.
Arial / Helvetica
Arimo
If you want a typeface with a smaller font size, you can consider Liberation Sans version 2.X. It has less characters.
Arial Narrow / Helvetica Condensed
You can use Liberation Sans Narrow, available at its own repository. Be aware that its license is complicated, therefore you should read it carefully. LICENSE AGREEMENT AND LIMITED PRODUCT WARRANTY GNU GENERAL PUBLIC LICENSE
Times New Roman / Times
Tinos
If you want a typeface with a smaller font size, you can consider Liberation Serif version 2.X. It has less characters.
Courier / Courier New
Cousine
If you want a typeface with a smaller font size, you can consider Liberation Mono version 2.X. It has less characters.
Georgia
Gelasio
Cambria
Caladea
Calibri
Carlito
Consolas
DMCA Sans Serif
Be aware that its creator is kind of a shithead, but the font is public domain.
Sources:
http://xahlee.info/js/metrically_compatible_fonts.html