How is the sun's equatorial circumference measured? How is the sun's equatorial circumference measured by scientists? 
 A: It is quite simple to get a reasonable measure of the sun's diameter, using a pinhole, a screen and the formula for experiment 2 on this At Home Astronomy article: "Finding the size of the sun and moon".
From the 'At Home Astronomy' article, the sun's diameter can be calculated as:
$$\frac{\text{Diameter of the sun's image}}{\text{Distance from the pinhole to the paper}}\times\text{Earth-sun distance} = \text{Diameter of the sun}$$
Edited to add:
The first recorded attempts to determine the distances and sizes of the Earth and Moon were performed by Aristarchus (310 - 230 B.C.), these were not very accurate (this information is also in the first link I gave originally).  Once the distance was known (or estimated), a measure for the size could be determined.
His method was to determine the angle to the sun when the moon was half full, hence at a right angle to the observer (a potential source of error) and measure the angle to the sun (as in the diagram below)

(Source)
I hope this clears up the inadequacies of my original post.
A: It should be simply as below:
$C = \pi d$
