Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Earth and Moon Rotation
Name: James
Status: Educator
Age: 30s
Location: N/A
Country: N/A
Date: N/A 

I have read your answer to "How fast does the earth and moon rotate." What is the formula for determining the rotational speed for any given latitude? I would like to use my latitude or one close to it for my students.

For ease of calculation, we will assume that the earth is a perfect sphere. This is a pretty good approximation; the surface IS extremely flat, and the oblateness at the equator is only a factor of about 0.3%.

The formula is
C=2 x Pi x R x Cos((Pi x L)/180)
if you calculate the cosine of an angle in radians (many computer spreadsheets use radians), or
C=2 x Pi x R x Cos(L)
if you calculate the cosine from the angle's measurement in degrees.

In this formula, Pi = 3.1415927..., L is the angle of latitude, and R is the radius of the earth, 6378 km.

Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois


This question is related to the one on "Earth Circumference" at different latitudes that I answered a few days ago. The radius (r) of a circle (that is parallel to latitude) at any latitude (assuming the Earth to be a perfect sphere) is the Earth's radius (3963.5 miles) times the cosine of the latitude angle. The circumference at the latitude is then 2 x pi x r. The Earth rotates once per 23 hours, 56 minutes and 4 seconds (approximately 24 hours). By determining circumference at any latitude and dividing it by the time in a day, you get the rotational speed.

Dr. Cook

Click here to return to the Environmental and Earth Science Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (, or at Argonne's Educational Programs

Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory