# Linearity in Weighing Instruments

You’re browsing technical documents to see if a weighing instrument’s specs match your requirements, and you keep seeing “linearity.” What is linearity? Why should you care? What does it mean in the weighing industry? Why are there plus and minus symbols? We’ll answer your questions about linearity, and help you understand why it’s relevant.

### What is Linearity?

We define linearity as the ability of a scale or balance to show the correct value throughout the weighing range. Linearity is typically tested by placing known weights on the balance from near zero to full capacity.

It is “linear” because if you graphed ideal results, you should get a fairly straight line. The plus and minus signs are a range of permissible error. Even the most accurate balances are not perfect all the time, but depending on the application, a small margin of error can be tolerated, as it is not high enough to cause major variations in results. So in our graph example, you would see the straight line (indicating perfect linearity) and two lines indicating the “+” and “-”. The actual results will show as an S curve. The scale’s results are permissible as long as they remain in that acceptable zone, even if they are not on the perfect line.

Linearity affects not only subsequent measurements, but measurements with important weight differences (for example, a lab balance weighing a small amount of powder, then a larger sample). You want to make sure that when you take advantage of the scale’s capacity, the margin of error and the accuracy of the scale or balance remains consistent whether you weigh a small envelope or a large, heavy package. Linearity ensures that no matter the amount of matter that is measured, the results will be accurate and precise as long as they’re within the capacity and readability.

### Linearity and Sensitivity

Because of the nature of linearity, linearity errors can sometimes be perceived as sensitivity errors. This is especially noticeable with laboratory balances, as they are very sensitive to the most minute changes and have low capacities. Sensitivity can be affected by a wide range of factors such as environmental conditions, mechanical or electronic issues or even infrequent calibration. It can be defined as the change in the result’s reading when compared to the change in load. Some balances allow users to use filters that adjust a balance’s sensitivity to compensate for moving subjects or vibrations.

Linearity, by contrast, is not affected by the environment, but by the changes in mass between samples. While you need to account for sensitivity when conducting linearity testing (to make sure your margin of error is due to the scale’s performance and not temperature changes, for example), linearity does not concern external factors and is only applicable to the balance’s ability to give consistent measurements when scaling masses. For example, you could put a 100g weight on a balance. Even if the balance read 130g, it could could still be linear if you put a 200g weight on and it read 230g.

### How is Linearity Different From Repeatability and Reproducibility?

Repeatability is the ability of the weighing instrument to give the same result for the same object under the same conditions every time, while reproducibility is the weighing device’s capacity to give the same results for the same object when measured by a different user. Linearity encompasses the scale or balance’s full capacity and ensures the results are reliable even when different amounts are measured.

For example, to test repeatability, you would keep measuring the same known mass to make sure you keep getting the same results. For reproducibility, you would measure the object, then have someone else measure the same object and check if your results differ. Linearity is a bit more complex. You’re not only testing that multiple known masses are within standard deviation, but also checking that the deviation does not change depending on the mass. If your standard deviation is of 0.1% for 1g, it needs to be the same amount for 1kg.

### How Can You Test Linearity?

It’s a little like calibrating a balance: you need to use multiple test weights that will approximate the weighing range of the instrument you are checking. The masses must be comparable to each other and within the range you are checking. Using known weights is an easy way to do it, so a calibration weight set is the ideal tool for the job. If you use inadequate weights, you could get unreliable data. Measure each mass and record the result exactly.

If a specific weighing range seems to be giving off more errors, you can make more tests specifically in that range as needed. You can create a table, or plot the results in Excel (you can find tutorials like this one if you’re not sure how to do this). Some organizations, especially laboratories, often have specialized software that can calculate the results. If that is the case, follow the procedures outlined by your organization.

You can graph the results with software, like our AdamDU data collection program, which is designed to work with scales and balances, and can export results to a wide variety of applications as needed. Trace one line for perfect results, one with the results you obtained for corresponding masses. Then trace a line for each of the highest and lowest standard deviations according to the specs of your weighing device. For example, if you’re using an EAB 124e, the linearity should be 0.0003g. Make sure you check the specs! Even if balances have the same capacity and readability, they could have different linearities depending on the brand or even the range. You plot one line for the “+” and one for the “-”. Your measurements should fall within these two lines. If they don’t, you can calculate the error margin and find where it appears.

### What Do I Do If the Linearity’s Error Margin is Too Wide?

You should make sure the weighing device is in a proper area, not close to heat sources, air currents, static electricity and other conditions that could affect readings. Even though linearity is not affected by outside factors, your scale may be giving you unreliable results interpreted as a linearity error because of poor conditions.

Clean and calibrate the scale. If the errors persist and are reproducible, you’ll have to call a technician to repair the weighing device.

Linearity is a complex topic worth understanding to get the most out of your scale or balance. If you have any questions, feel free to contact us. We’re at your disposal. Want to find out what the linearity on an Adam product is? Check out our data sheets.