Force, Mass, and Weight: What is the Difference?
Force, mass, and weight are related concepts in physics, yet they are distinct and often misunderstood.
Introduction to Difference Between Force, Mass, and Weight
Figure 1. NBS Document Regarding Force Calibration Services
I recently read an old NBS unpublished Provisional Document of "The Force Calibration Service" provided by the National Bureau of Standards (NBS) and given to Morehouse.
The document is dated 1982-1983. For a document over 40 years old, there were a lot of interesting concepts that we once thought to be true and some that many still do not understand today.
The document is full of discussion and policy from what is now the NIST force group.
These discussions range from the treatment of zero to the need for "customer enlightenment" regarding the differences between Force, Mass, and Weight.
Considering many discussions we have been privileged to have this year with our customers regarding various topics, two seem to occur frequently.
The first is many are making measurements and still removing adapters from their load cells, which can create a lot of measurement errors.
The second seems to come back to someone calibrating a load cell without applying the proper corrections to make a force measurement.
Thus, a forty-plus-year-old document seems very relevant today as the "customer enlightenment" regarding Force, Mass, and Weight needs a boost or refresher for many.
This article will highlight the differences in Force, Mass, and Weight using the NBS terms and compare them with definitions forty-plus years later to see what has changed and discuss how to properly use mass weights for force applications.
Force Definitions
Figure 2 Definitions from the NBS Force Document
Gravitational Force (1983) – the attraction of the Earth on a mass, causing the mass (if unrestrained) to accelerate.
Static Force (1983) – a steady or unchanging force, such as the Force necessary to balance exerted in a load spring or Force developed by a stationary mass subject to the Earth's gravitational field.
Force – mass * acceleration. 1N is the Force required to accelerate 1 kg to 1 meter per second per second in a vacuum.
Force weight - "Deadweight" - a physical item with a calibrated mass producing a force close to a nominal force value. Force weights typically do not have an accuracy class. Force weights are usually custom-made (amount of material in weight adjusted) to apply a vertical nominal force at a specific location.
For instance, A 5 Newton deadweight might have a conventional mass of approximately 49 kg.
Mass Definitions
Mass (1983) – the quantity of material present in a physical object. It is a scaler quantity independent of the physical body and its location in the universe.
Mass (2024) - is a fundamental property of matter that quantifies the amount of matter in a physical object. It is one of the seven base quantities in the International System of Units (SI) and is measured in kilograms (kg).
The official definition of the kilogram, which is the SI unit of mass, is:
It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 x 10–34 when expressed in the unit J s, which is equal to kg m2 s–1, where the metre and the second are defined in terms of c and ΔνCs.
Mass (Simplified) – mass is a measure of the amount of matter in an object. Mass is the amount of something (volume * density). The SI unit of mass is the kg. The customary unit is the pound. M = True mass of the artifact. The term "mass" is always used in the strict Newtonian sense as a property intrinsic to matter. This property is sometimes referred to as "true mass" or "mass in a vacuum" to distinguish it from the conventional (apparent) mass (CM).
Mass weight – meets OIML R111-1 requirements. The mass weight is a physical item with a conventional mass close to a nominal value. A 5 kg weight will have a nominal value of 5 kg and a calibrated conventional mass value within its class accuracy to the nominal value.
Weight (1983) - is the downward Force exerted by a physical object, a vector quantity dependent upon the strength of the gravitational field, the relative densities of the object, and the medium in which it is immersed.
Weight - the Force acting on a body due to gravity. It is defined as the vector quantity equal to the product of the mass of the body and the local acceleration due to gravity.
Key Difference Between Force, Mass, and Weight
Simplified Example of Difference Between Force, Mass, and Weight
Think of mass as the "stuff" things are made of.
Gravity pulls on that "stuff," and that pull is called weight.
A force (like weight) happens when something pushes or pulls on the "stuff."
Figure 3 Morehouse Cartoon Demonstrating a Common Error of Calibrating Load Cells with Conventional Mass Weights
A load cell calibrated with weights corrected for force can be used in any location without needing additional adjustments for local conditions, making it highly practical for use anywhere in the world or universe.
Calibration using Force eliminates the need for repeated corrections when moving between locations, saving time and reducing the risk of errors.
However, weights used to measure Force require corrections for local gravity, air density, and material density.
These weights, once adjusted, cannot be used in other locations without recalibrating for the new gravity and air buoyancy conditions.
In contrast, force-measuring instruments calibrated with force weights are universally applicable and can be used anywhere without additional corrections.
Measurement Traceability of Force
The traceability of any force measurement ultimately comes from mass. The weights (masses) used to exert the Force come in several different types:
- Force weights – often called "deadweight force" or "primary standards" are machined and adjusted so that they will exert a nominal force at a specific location. These force weights are often used for torque (force x length) as they exert that nominal Force at the end of an arm with a known length.
- Pressure weights – custom-built weights to exert a specific nominal pressure when mated with a specific piston at a specific location.
- Mass weights are typically OIML-compliant weights with nominal conventional mass. These usually come in sets that adhere to a specific class (accuracy).
Mass weights are commonly used to calibrate balances and scales to conventional mass values.
That is their primary purpose.
If a laboratory calibrates force using mass standards, the applied Force must be calculated appropriately, accounting for the local acceleration of gravity, material density, and buoyance Force.
Force and mass are related, though they are not the same.
A weight with a true mass of 1 kg will have a true mass of 1 kg anywhere in the world.
Its conventional mass, used for calibrating balances, will slightly change (a few mg, a few ppm) worldwide due to air density changes.
The vertical Force produced by a weight with a true mass of 1 kg will vary by as much as 0.539 % worldwide because of the variation of local gravity.
This is because gravity is not constant over the surface of the Earth.
The most extreme difference is 0.539 % between the poles and the equator (983.2 cm/s2 at the former compared to 978.0 cm/s2 at the latter).
To simplify this into an example:
You calibrated a crane scale (Force, lbf) using mass weights and corrected the mass weights for the calibration location (calibrated the crane scale correctly).
Since it was calibrated correctly, the crane scale will indicate the correct Force (lbf) at any location.
If you did not correct the mass weights for the location of the calibration, then it was calibrated for mass (not force lbf), and the scale will only be correct for mass at that one location where it was calibrated.
This measurement could be off as much as 0.539 % of applied Force!
It will rarely indicate lbf correctly.
The one exception might be at sea level and 45 degrees latitude, where mass (lb) and Force (lbf) are similar enough that the resolution of the crane scale likely contributes more to the measurement uncertainty.
Conversions
We hope this explanation clarifies the topic and ensures that anyone using weights for force measurements understands the importance of correcting those weights before applying them in force-related applications.
Table 1 Formulas for computing Force or True Mass
M = true mass
g = local gravity at a fixed location, m/s2.
Table 2 – Formulas for computing Force or Conventional Mass (EURAMET-CG-4)[1]
MC = Conventional Mass
ASTM E74 & E2428 Equation to Calculate Force
Morehouse Spreadsheet to Convert Mass to Force
Because many of these formulas may seem overwhelming, we have simplified things as much as possible.
Morehouse has a free spreadsheet tool to help with conversions from Force to mass and mass to force.
The spreadsheet allows load cells to be converted from Force to mass and provides formulas to compute Force applied from mass weights.
The Morehouse spreadsheet can be found here for anyone wanting an open, unlocked spreadsheet to help with these conversions.
Note: The spreadsheet is not locked and can easily be changed. Use at your own risk.
Difference Between Force, Mass, and Weight Conclusion
Force, mass, and weight are closely related concepts in physics, but they are distinct and often misunderstood.
Here is a simplified summary to understand their differences:
- Mass: Mass is the amount of matter in an object. It does not change, no matter where you are in the universe. It is measured in kilograms (kg) and is a scalar quantity, meaning it has no direction.
- Weight: Weight is the Force of gravity pulling on an object's mass. It depends on the local gravitational field, so your weight can change if you go to a place with different gravity, like the Moon. Weight is measured in newtons (N) and is a vector quantity, meaning it has direction (toward the center of gravity).
- Force: Force is any push or pull acting on an object. It is measured in newtons (N) and is calculated using the formula F=ma, where m is mass and a is acceleration.
When calibrating instruments like load cells to measure Force, it is important to use weights or make the corrections needed for local gravity, air density, and material density.
Without proper corrections, measurements can be inaccurate up to 0.539 % in error just from local gravity.
More Information about Morehouse
We believe in changing how people think about Force and Torque calibration in everything we do.
This includes setting expectations and challenging the "just calibrate it" mentality by educating our customers on what matters and what may cause significant errors, such as not understanding what Hysteresis is.
We focus on reducing these errors and making our products simple and user-friendly.
This means your instruments will pass calibration more often and produce more precise measurements, giving you the confidence to focus on your business.
Companies around the globe rely on Morehouse for accuracy and speed.
Our measurement uncertainties are 10-50 times lower than the competition, providing you with more accuracy and precision in force measurement.
We turn around your equipment in 7-10 business days so you can return to work quickly and save money.
When you choose Morehouse, you're not just paying for a calibration service or a load cell.
You're investing in peace of mind, knowing your equipment is calibrated accurately and on time.
Through Great People, Great Leaders, and Great Equipment, we empower organizations to make Better Measurements that enhance quality, reduce risk, and drive innovation.
With over a century of experience, we're committed to raising industry standards, fostering collaboration, and delivering exceptional calibration solutions that build a safer, more accurate future.
Contact Morehouse at info@mhforce.com to learn more about our calibration services and load cell products.
Email us if you ever want to chat or have questions about a blog.
We love talking about this stuff. We have many more topics other than expressing SI units!
Our YouTube channel has videos on various force and torque calibration topics here.
References
Provisional Documentation of the Force Calibration Service provided by the National Bureau of Standards
EURAMET-CG-4 Uncertainty of Force Measurement
ASTM E74-18 Standard Practices for Calibration and Verification for Force-Measuring Instruments
