Contents

## Related Tools

## User Guide

This local gravity calculator determines the theoretical acceleration due to gravity at a particular location using a formula for determining the gravity at a certain latitude position and height above or below mean sea level in free air.

This calculator should only be treated as an approximation of local gravity, and does not include further corrections for elevated flat terrain above mean sea level , or below the ground or surface of an ocean, nor does it account for the density of the local geology, which would be necessary for a more precise determination.

#### Formulas

The formulas used by this calculator are based on the International Gravity Formula IGF) 1980 from the parameters of the Geodetic Reference System 1980 (GRS80), which determines the gravity from the position of latitude, and the Free Air Correction (FAC) which corrects for height above and below mean sea level in free air.

IGF = 9.780327 (1 + 0.0053024sin^{2}Φ – 0.0000058sin^{2}2Φ)

FAC = -3.086 x 10^{-6} x h

g = IGF + FAC

###### Symbols

- g = Theoretical local gravity
- IGF = International Gravity Formula
- FAC = Free Air Correction
- Φ = Lattitude
- h = Height relative to sea level

#### Latitude Coordinate

Enter the position relative to the equator in decimal degrees. Latitude can only be specified between -90° and 90°. You can determine the latitude position by going to Google Maps on a desktop web browser, and right clicking your mouse on the required location, and then selecting “What’s here?”, which will display the latitude value followed by the longitude value as decimal values.

#### Height above Sea Level

Enter the known height above or below mean sea level in metres or feet for the required location. If you do not know the height above sea level you should be able to obtain it from your national geological survey maps. If the height is below sea level then prefix the height value with a minus (-) sign.

#### Local Acceleration due to Gravity

The theoretically determined value for the acceleration due to Earth’s gravity at the specified location is displayed here in metres per second per second (ms^{-2}).

###### Error Messages

- “
*Nan*” (Not a number) – This means you have not yet completed all the required fields. - “
*Latitude not valid*” – The Latitude co-ordinate must be between -90° and 90° and written as a decimal value, e.g. The Royal Greenwich Observatory location has a latitude of 51.4778°. - “
*Height above Everest?*” – You cannot enter a height above sea level greater than the height of Everest, the highest point on land. - “
*Height below Dead Sea?*” – You cannot enter a height below sea level which is lower than the height of the Dead Sea, the lowest point on dry land.

## Help

### More precision

*How do you determine a more precise value of local gravity?*

Although latitude is a major factor in determining the local gravity, the local geology and terrain also influence variations in local gravity. The most accurate value of local gravity would be the one continually measured by your national geological survey organisation nearest to you, such as the British Geological Survey (BGS) or the U.S. Geological Survey (USGS) and then corrected for your location.