Microstrip Substrate Equations
You can work these formulas manually, or download this great free microstrip calculator (TX Line) from AWR.

Equations are given for calculating the effective width and height prior to plugging the dimensions prior to plugging them in to the equations for effective dielectric constant and then for calculating the impedance.

Here is a really nice summary of many controlled impedance line equations, by Rick Hartley.

RF / Microwave PC Board Design and Layout

Be aware that there are many microstrip impedance calculators on the Internet that give sometimes widely varying results. Be sure of which one you finally decide to use. Most claim to use some or all of these formulas these formulas, but I have discovered ones, for instance, that appear to mistakenly substitute 0.4 for 0.04 in the εeff formula for the W/H<1 case.

Effective Width and Height
Microstrip calculation equation - RF Cafe
RF Cafe: Microstrip calculation equation
Microstrip equations - RF Cafe Wavelength Microstrip substrate dimensions for impedance calculation - RF Cafe
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Microstrip calculation equation - RF Cafe