I found my initial estimate of the drag coefficient of a dirt bike may have been a little high. I have read that motorcycles have drag coefficients in the range of 0.6 to 1.0. Sport bikes have drag coefficients of around 0.6. Dirt bikes would be on the higher end. I will now use 0.95 for my estimate.**

You can calculate theoretical top speed for any bike, but you have to do a couple important estimations, namely, the projected frontal area of the bike and rider and the drag coefficient. You can use a frontal picture of yourself seated on your bike and a ruler to help estimate area by scaling everything.

The drag force on a bike & rider is:

F = (1/2)(rho)(V²)(A)(Cd)

Where
F is drag force (Newtons)
rho is air density (kg/m³), about 1.2 kg/m³ at sea level
V is velocity (m/s)
A is projected frontal area of bike and rider
Cd is drag coefficient (dimensionless). A dirt bike will be on the higher end of range of typical drag coefficients for motorcycles (I will use 0.95). Things like fenders, shrouds, helmets without full face shields, loose jackets, etc. all create little pockets that can increase the drag coefficient. For example, an anemometer with hemispherical cups spins because the drag coefficient for air blowing into the cup is about 1.4 and the drag coefficient for air blowing around the outside of smooth hemisphere of the cup is about 0.4.

The power required to maintain a given speed is the drag force, F, multiplied by the velocity.

P = F · V
P = (1/2)(rho)(V³)(A)(Cd)

Where
P is power (Watts).
745.7 W = 1 horsepower

For example, I will use my bike:

My XR350 can produce about 30 or so horsepower (although Honda claims 31.8 horsepower), or about 22,371 Watts. Horsepower at the rear wheel would be the best number to use, since this would take drivetrain friction out of the picture. I estimate around 0.7 m² projected area, and a drag coefficient of 0.95.

22,371 W = (1/2)(1.2 kg/m³)(V³)(0.7 m²)(0.95)
V = [(22,371 W)/(1/2 · 1.2 kg/m³ · 0.7 m² · 0.95)]^(1/3)
V = 38.27 m/s = 85.6 mph (1 m/s = 2.2369 mph)

This means my bike should have enough power to propel me up to 38.27 m/s, which is 85.6 miles per hour. According to my shop manual, my engine produces peak horsepower at 7000 rpm. I need to gear my sprockets so that my engine's power peak at 7000 rpm will occur when the bike hits 85.6 mph in sixth gear. There is a gearing calculator in the tech section called Top Speed (or you can do it by hand):
Click here for link to working excel worksheet: Motorcycle Gearing Worksheet

Motorcycle Gearing Worksheet
	Values (Enter)	Total Ratio		Min. Speed	Max. Speed	Speed at Max Power	Min. Speed	Max. Speed	Speed at Max Power	Chain size	Chain pitch mm	Chain pitch inch
Primary Drive Ratio	1.651		Gear	(MPH)	(MPH)	(MPH)	(KPH)	(KPH)	(KPH)	428	12.7	0.5
1st Gear Ratio	3.083	17.452	1st	9	35	30	0	56	47	520	15.875	0.625
2nd Gear Ratio	2.125	12.029	2nd	13	51	43	20	81	69	525	15.875	0.625
3rd Gear Ratio	1.666	9.431	3rd	16	65	55	26	104	88	530	15.875	0.625
4th Gear Ratio	1.333	7.546	4th	20	81	68	32	130	109	532	15.875	0.625
5th Gear Ratio	1.115	6.312	5th	24	97	82	39	155	131	630	19.05	0.75
Front Sprocket (Teeth)	14	3.429		Approx.						632	19.05	0.75
Rear Sprocket (Teeth)	48		Chain	Number
Chain pitch	15.875		Length	of links	Chain pitch and countershaft to rear axle distance can be in mm or inches,
Countershaft to rear axle dist.	630		1763.86	111.1	the chain length will be returned in the same units.
Shortest possible	620		1744.05	109.9
Longest possible	640		1783.67	112.4	NB. Chains always have an even number of links, bear this in mind when
Wheel Rim Size (Inches)	18				looking at the 'Approx. Number of links' figures. If necessary, adjust the
Tyre Width (MM)	120				Countershaft to rear axle dist.' figure until you're happy with the number of links.
Tyre Depth (%)	80
Engine Minimum RPM	2,000
Engine Maximum RPM	8,000	Ü Enter known values in the pink column. The yellow and blue values are calculated from the pink ones.
Maximum Power RPM	6,750

You can enter your rear tire outer diameter and transmission ratios. Then, the remaining variables that determine speed are sprocket gearing and engine rpm. For my bike, I would use 7000 rpm and work out what sprockets I needed to use to hit 85.6 mph at that engine speed in sixth gear. This should be a good starting point towards gearing the sprockets for maximum top speed capability. Minor changes in sprocket gearing, either up or down, will probably be needed for the very best speed.

As an alternative to make things quicker, here is chart I made showing Horsepower To Overcome Drag vs. Speed, at an air density of 1.2 kg/m³. Use the line that is the closest match for the product of your projected frontal area and drag coefficient, or interpolate for more accuracy: