Bath-Scales weight or mass?

I read that bath scales measure body weight and not mass which means they measure m*g and not m.

1. If I got a reading of 50 kg, does that mean that my mass is nearly 5?

2. Units of m*g aren't kg so why we say my weight is 50 kg? shouldn't it be called like my weight is 500 N?

• FWIW, some scales are actually balances, so they do measure mass, not weight. But that's not true of typical bathroom scales. Commented Oct 21, 2020 at 11:00
• @PM2Ring thanks
– dan
Commented Oct 21, 2020 at 11:13

2 Answers

Yes, typical bathroom scales measure weight $$mg$$, not mass $$m$$. But for convenience they are calibrated to show a reading in mass units, eg kilograms (or pounds).

So if the scales indicate that your "weight" is 50 kg that really means that your mass is 50 kg. Your weight is your mass times the gravitational acceleration, which is approximately 10 m/s² (more precisely 9.80665 m/s², but it varies slightly depending on your location), so your actual weight is (roughly) 500 newtons.

However, most people aren't physicists or engineers, so it wouldn't be very practical to tell them you weigh 500 newtons when they ask you your weight. ;) Besides, when people ask you your weight, they (probably) really want to know your mass. Common language treats mass and weight as synonymous, but when doing physics or engineering we need to be more careful with our terminology.

• I think you made a mistake how could be my mass be bigger than my weight? the weight is m*g and it's bigger than m (mass) for sure
– dan
Commented Oct 21, 2020 at 11:12
• @dan Oops! I made a typo. They can be hard to notice when you're typing on a phone... Commented Oct 21, 2020 at 11:17
• the second paragraph still has contradictions, if my mg is 50 then my mass is 5kg
– dan
Commented Oct 21, 2020 at 11:21
• @dan No, I fixed the typo, and the 2nd paragraph has no contradictions. If your mass is 5 kg then you must be a baby. :) If the scales say you weigh 50 kg, then your mass $m$ is 50 kg and your weight $mg$ is 500 N. Commented Oct 21, 2020 at 11:31
• @dan Yes, but I also said that the scales are calibrated to show a reading in mass units. So even though they are internally measuring your weight, the display on the scale tells you your (approximate) mass. But if you stood on those scales on the Moon they'd give a reading of 8.26 kg instead of 50 kg, because the Moon's gravity is much smaller than the Earth's so your weight is lower there, even though your mass is the same. Commented Oct 21, 2020 at 12:53

Typical bath scales do measure weight and report the weight in units of mass. These scales will report a lower weight for the same mass at the equator compared to the poles and at a high altitude compared to a low altitude. Usually these errors are far below the precision of the reported weight.

However, there are similar scales that do measure mass. These can usually be distinguished by the fact that they must be calibrated onsite. Once they are calibrated on-site then the same mass will give the same reading on the equator or the poles, despite the different weights. For example, NTEP class 1 scales which are certified legal for trade and are sensitive enough to detect differences in g at different locations. Even though such scales are sensitive to the local value of g, they can correctly be said to measure mass after calibration.