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When someone asks us about converting force to mass, Morehouse can now say we have an app for that. Not only will our app convert force to mass, but it will convert mass to force as well as convert units. It will convert force, torque, and pressure units. Anyone interested in downloading the app can visit the google play store https://play.google.com/store/apps/details?id=com.mhforce.localgravity or scan the QR code below at the end of this article.

Let’s look at why this app is needed.


Using Mass weights to calibrate a force-measuring instrument can result in large measurement error.

When metrologists talk about measurement error, we’re talking about the difference between the nominal value and what the instrument is reading.  If 10,000 lbf is applied to a force measuring device and the readout displays 10,002 lbf, then the device has a 2 lbf bias. If we load the same force measuring device to 10,002 lbf, we will have applied 10,000 lbf. This is a measurement error, and there can be many different causes. After speaking with several professionals inside the weighing industry, it has come to my attention that some labs use mass weights to calibrate force devices. These include dynamometers, crane scales, hand-held force gauges, and others. This can result in significant measurement error.

Let’s quickly review the difference between mass and force. Mass, under almost every terrestrial circumstance, is the measure of matter in an object. Measuring force takes additional factors into account: air density, material density, and gravity. It’s the effect of gravity which can produce significant errors when comparing mass and force measurements.

It is very important that the gravitational value for the Laboratory is established. The effect of not doing this could be a variation in the force produced by the weight of perhaps 0.1 % or more of reading. It is therefore strongly recommended that you establish the local value of gravity (g) for your Laboratory and use weights that have been calibrated at that gravitational constant.

Gravity is not constant over the surface of the earth. The most extreme difference is 0.53 % between the poles and the equator (983.2 cm/s2 at the former compared to 978.0 cm/s2 at the latter). A force measuring device calibrated in one location using mass weights then deployed somewhere else will produce different strains on the physical element. The resulting measurement errors can be significant.

Correcting for the difference in force and mass measurements is possible. When a device is adjusted for force measurements, the device will measure force without additional error for gravity correction, air density correction and so on needed.

The Morehouse app will use your exact coordinates, go to NOAA’s website, and convert the mass value to force using this formula.

Force = M x g / 9.80665 m/s2 (note: to properly convert mass to force material density and air density should be known) This formula will have additional errors that are likely less than 0.02 %. For more information on mass to force please read https://www.mhforce.com/BlogPost/PostDetails/180?title=Force-Applications-for-Mass-Reference-Standards-


Pictured Above: Morehouse SCM-60 Aircraft and Truck Scale Calibrating Machine


Using force instruments to calibrate in mass has a similar measurement error.

Forces are defined by Newton’s second law of motion is expressed by F =kMA. Forces are not the same as or can they be substituted for mass without correction. Phillip Stein once wrote in his paper Gravity of the Situation, “Some measurements and calibrations require knowledge of little g. Errors and uncertainties in little g fall right to the bottom line (a 1% error in g results in a 1% error in the force reported) and therefore exert an important influence on the correctness of measurement results.”

A common example of these measurement errors occurs with scales (a mass measurement device). If 1000 lbs mass is used to calibrate a scale at Morehouse and that scale is shipped to Denver, CO, it would have to be calibrated again or corrected by formula to obtain the proper mass. Just comparing the gravity in York (9.801158 m/s2) and Denver (9.79620 m/s2), we find a difference of about 0.05 %. Without correction, 1000 lbs applied would read as 999.5 lbs. If the accuracy of the scale were 0.01 %, then the device would be at least five times greater than the accuracy specification.

Converting Force to Mass requires knowing the local gravity where the weighing takes place.

A mass correction factor can be calculated to convert force to mass when the transfer standard is used at a location where the gravity is known as follows:

Mass Correction Factor = (9.80665/g)