Local Gravity: How to Calculate Yours in 3 Minutes

How to Calculate Local Gravity
 

Introduction

In Metrology, knowing your local gravity is important if you are performing comparison measurements that involve forces that are influenced by gravity.

Established at the third General Conference on Weights and Measures in 1901, the standard gravity on Earth is 9.80665 meters per second squared, or 32.174 feet per second squared.

However, standard gravity only applies to an object or body at sea level and geodetic latitude of 45 degrees. Most likely, this does not apply to your laboratory; so, you may want to consider calculating your own local gravity.

Measurements that may be influenced or impacted by local gravity, where the rate of acceleration is gravity;

  • Force
  • Weight
  • Torque
  • Pressure

 
 

What is Standard Gravity

According to Wikipedia, standard gravity is the nominal gravitation acceleration of an object in a vacuum near the surface of the Earth.

According to NIST, the standard acceleration of gravity is exactly 9.80665 m/s2 which is approximately 32.17405 ft/s2.

 
Standard Gravity Value 9.80665 m/s/s NIST

 
 

Why Calculate Local Gravity

Depending on the measurement functions and processes that you perform, you may need to know your local gravity. It may significantly affect your results.

For example, take two pressure gauges and calibrate them at different locations where there is a significant difference in local gravity. The results will be different unless they are both corrected back to standard gravity.

Therefore, if you do not take local gravity into consideration, you may end up with erroneous results that may cause you to report the wrong statement of conformance.

If you perform the following calibrations, you should know your local gravity:

  • Calibrate Pressure items with a Dead Weight Tester,
  • Calibrate Torque devices with wheels, arms, pans, and weights,
  • Calibrate Force items with dead weight.

 
 

How to Calculate Local Gravity

To find your local gravity, follow the steps listed below:

  1. Find your Latitude and Longitude,
  2. Find you Elevation above Sea-Level,
  3. Calculate your Local Gravity

In this section, we are going to dive deeper into each of these steps, so you can calculate your local gravity.

 

1. Find your Latitude and Longitude

Since local gravity is affected by latitude, you will need to find know your location’s geographic coordinates. With today’s GPS technology and the internet, this task has become very easy.

I recommend using on the following options:

  1. Google Maps
  2. GeoPlaner

 

Google Maps

All you need to do is go to Google Maps, type in your physical address, and identify your latitude and longitude coordinates from your browser’s address bar.

Just follow the steps below to find your latitude and longitude in Google Maps:

  1. Go to Google Maps,
  2. Type in your address,
  3. Find your coordinates in the browser’s address bar

 
Find Latitude and Longitude via Google Maps

 
Or, you can just go to Google Maps and let geolocation tell you.

Take a look at the browser bar in the image below. I went to google maps, waited about 3 seconds, and my latitude, longitude, and elevation automatically populated with the web address.

 
Google Maps Latitude, Longitude, and Elevation

 
If you are having a little trouble, read this guide from Google.

 

Geo Planer

For a one-stop-shop to easily find your geodetic coordinates, use the Geoplaner website. It is a great tool to get all the information that you need to calculate local gravity.

Just follow the steps below to find your latitude and longitude in Geo Planer:

  1. Go to Geo Planer,
  2. Type in your address and click the “ok” button,
  3. Find and record your coordinates in “dd.ddddd” format.

Click the link below and enter your physical address to find your geodetic coordinates.
https://www.geoplaner.com/

 
Enter Address at Geoplaner

 
After you enter your physical address, this tool will give you your latitude and longitude in several formats. I recommend that you record the coordinates in ‘dd.ddddd’ format.

 
Find Latitude and Longitude via Geoplaner

 

2. Find your Elevation Above Sea-Level

The next variable that you will need to find is your elevation above sea-level. For many, this task can be a little tricky; but, I will show you how to find elevation easily.

In the past, you had to go to the local library or local government offices to view topographic maps. Today, technology and the internet have made this task much easier.

The Geoplaner website will give you your elevation above sea level which is why I like to use it. It is an all-in-one tool to find your latitude, longitude, and elevation.

Just record your elevation in meters. Use the image below for reference.

 
Find Elevation via Geoplaner

 

3. Calculate your Local Gravity

Now that you have identified your latitude, longitude, and elevation above sea-level, it is time to calculate local gravity. If you prefer, you can use equations; or, you can use the internet and gravity calculators to simplify the task. For efficiency, let’s use an online calculator.

To calculate local gravity online, I recommend using the NOAA Surface Gravity Prediction calculator.

In the images below, I am going to use the NOAA Surface Gravity Prediction website to calculate local gravity. You will need to enter your latitude, longitude, and elevation that you recorded in the previous steps.

To calculate your local gravity, follow the steps listed below:

  1. Visit the NOAA Surface Gravity Prediction website,
  2. Enter your latitude,
  3. Enter your longitude,
  4. Enter your elevation,
  5. Click the “Let’s go” button, and
  6. Record your local gravity.

 
NOAA Local Gravity Calculator

 
After clicking “Let’s go,” you will be directed to a webpage that looks similar to the image below. This page will give you your local gravity. Print the page and keep it for your records.

 
NOAA Gravity Calculator Result

 
 

Calculate Local Gravity Using An Equation

If you prefer to calculate local gravity with an equation, I recommend using the equation that used to be published on the National Physical Laboratory website.

http://www.npl.co.uk/reference/faqs/how-can-i-determine-my-local-values-of-gravitational-acceleration-and-altitude-(faq-pressure)

This webpage no longer exists (or has been moved). However, you can use the image below to get the equation.

 
NPL local gravity equation

 
Using Microsoft Excel, I created a calculator to calculate local gravity using the equation above including the estimate of uncertainty associated with the value of gravity.

 
local gravity calculator by ISOBudgets

 
If you want a copy of this calculator, click the link below and enter your email address to download it.

 
Click here to download the
local gravity calculator for free!

 
 

Local Gravity Calculators

To calculate local gravity (without using long equations), you will want to use a calculator. There are several free calculators available online. Here is a list of the best local gravity calculators online:

 
 

Comparing Local Gravity Calculators

While there are several local gravity calculators available online, not all of them give the same result.

Here is a chart comparing each gravity calculator’s results for the same location (i.e. latitude, longitude, and elevation).

 
local gravity calculator comparison chart

 
As you can, some calculators give different results. Here is an overview of the results:

  • BGI and PTB results are nearly identical.
  • NOAA and PTB results are relatively similar but do not agree with the NPL equation.
  • NPL, SensorOne, Walter Bislin, and ISOBudgets excel calculator yield the same results and most likely use the same equation.
  • FlowSolv calculator result is significantly different because it only allows you to enter your latitude and uses a default elevation of 100m.

 
 

Convert Gravity from Milligals to m/s2

Some of the local gravity calculators online give you the results in milligals. However, I prefer to have the results in meters per second squared. Therefore, I divide the milligals result by 100,000 to convert gravity to meters per second squared.

 
convert gravity in milligals to meters per second squared

 
To convert from milligals to meters per second squared, follow the instructions below:

  1. Find your gravity in milligals,
  2. Divide the result by 100,000, and
  3. Record your result in m/s2.

 
 

Correcting for Local Gravity

When you need to correct your measurement results for local gravity, use the equation given below. Typically, this is quite common for pressure, torque, and force (e.g. weight).

 

Standard Gravity to Local Gravity

If you need to correct your results for local gravity, all you need to do is calculate the gravity correction factor using the equation below.

 
correct standard gravity to local equation

Where,
GCF = Gravity Correction Factor
gL = local gravity
gS = standard gravity (9.80665 m/s2)

 
To convert results from standard gravity to local gravity, follow the steps below:

  1. Calculate your local gravity,
  2. Divide your local gravity by standard gravity,
  3. Multiply your measurement result by your gravity correction factor.

 

Local Gravity to Standard Gravity

If you need to correct your results back to standard gravity, all you need to do is inverse the previous equation.

 
correct local to standard gravity equation

Where,
GCF = Gravity Correction Factor
gL = local gravity
gS = standard gravity (9.80665 m/s2)

 
To convert results from local gravity to standard gravity, follow the steps below:

  1. Calculate your local gravity,
  2. Divide standard gravity by your local gravity,
  3. Multiply your measurement result by your gravity correction factor.

 
 

Conclusion

Knowing your local gravity is important. It can influence your measurement results, especially if they are directly or indirectly related to Force.

In the past, finding your local gravity could be challenging and expensive. Today, the internet makes this task quick and painless.

In this guide, you should have learned how to easily calculate your local gravity online in less than 5 minutes. Plus, I have given you plenty of information to help you correct your measurement results and reduce your uncertainty.

I hope this guide will become a helpful and handy reference guide. If you feel that I have left something out, please email me to recommend additional information.

 
This article was updated on 03/14/2020.

About the Author

Richard Hogan

Richard Hogan is the CEO of ISO Budgets, L.L.C., a U.S.-based consulting and data analysis firm. Services include measurement consulting, data analysis, uncertainty budgets, and control charts. Richard is a systems engineer who has laboratory management and quality control experience in the Metrology industry. He specializes in uncertainty analysis, industrial statistics, and process optimization. Richard holds a Masters degree in Engineering from Old Dominion University in Norfolk, VA. Connect with Richard on LinkedIn.

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