# How does 1Kn of force equal 100 kg in weight

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In the rope access industry everything is rated in kn of force. We can directly equate this to 100 kg when looking at working load limits on the slings in which we use to hang off of. Everyone always says you don’t need to know why, you just need to know that it does. I would like a simple way of explaining it to the new people coming into my industry.

In: 1 A kg is a measure of mass, a kN is a measure of force. To get force you multiply the mass by the acceleration of gravity (9.81 m/s*s). 9.81 is pretty close to 10, so they are simplifying it when they say 1kN.

I.e. 100 kg x 9.81 m/s*s = 981N or 0.981kN

9.81 is pretty close to 10, so they’re just rounding it up to 10.

100 kg x 10 m/s*s = 1000N or 1kN

In other words if you want the mass the rope is rated for, just take it’s force rating and divide by 10. Kilogram is a measure of mass, not weight. Newton is a measure of force. Weight is the term used for the force of gravity acting on a mass. The weight of 100kg of mass in earth’s gravity is approximately 1000N or 1kN. (Approximate because it is probably closer to 980N)

For simplicity’s sake, it is usual to simply take the mass in kg and multiply by 10 to get the weight. I’d guess that this is important in any situation where something needs to oppose the weight (like carrying or supporting it) kg is technically a unit of mass, not weight. Weight is force which is mass x acceleration. In this case acceleration is gravity which is 9.8m/s^2

1kg x 9.8m/s^2 = 9.8N ~ 10N

Confusingly what we mostly think about when we think of kilograms is the weight of an object with mass 1kg. Such an object would still have a mass of 1kg on the moon, but its weight would be lower. The newton (and by extension the kilonewton) is a unit of force. In case of ropes, it’s important that you know how much force it can take, in case you’re doing something else than just hanging off of it (eg swinging a mass around). In that case, you could calculate the tension in the rope, and pick one that works.

But if you’re just hanging on it, then it’s a lot easier. In that case, the only force we’re worried about, is gravity. So to see why 1kN of force is (roughly) equivalent to 100kg of mass, we need to look at one of Newton’s laws: F=m*a. Force is mass times acceleration. We already know what the maximum force the rope can handle is. And here on Earth, the acceleration due to gravity is around 9.81m/s². It can differ from location to location, but that’s good enough for most cases. So to find the mass that corresponds to the 1000N, we divide that by 9.81. Now, this isn’t all that easy to do when out in the field. So usually, the gravitational acceleration gets rounded to 10. This is less accurate, but more safe. If the rope can hold 1000kN, then it can hold a mass of about 102 kg. So by saying it’s a mass of 100kg, it makes the calculation easier, and since you round the end result down, it doesn’t make it less safe. They match perfectly because one is based off of the other.

1 Newton is the weight that a 1-kilogram mass has in Earth gravity.

(That same 1 kg would only have about 0.377 Newtons of weight on Mars.) Newtons (N), and extended units like kiloNewtons (kN), are units of force. When we talk about weight, we are usually talking about the force which is exerted by a mass in a gravitational field, although you could also be talking about the force exerted by an object which is accelerating (e.g. in an elevator). So, your weight can change. You weigh less on the moon, and you weigh more in an accelerating rocket. Your weight is dependent on the acceleration you are experiencing. Your mass, however, does not change. 1 kg on Earth is 1 kg on the moon is 1 kg in the rocket. At the Earth’s surface, at sea level, the average gravitational acceleration is 9.80665 m/s^2 . So, your 1 kN of force corresponds to (1000.00 N) / (9.80665 m/s^2 ) = 101.972 kg. This is approximately a factor of ten.

Note that this applies in the static case for an object subject to gravity, but in rope work, you also have to deal with dynamic effects. A falling mass being brought to a stop by a rope in a short period of time corresponds to a large acceleration, and thus large forces which the rope system must sustain. You have two different things here the force that you can pull on a rope (without breaking it) and what sort of mass would pull with such a force if you attached it to the rope.

A 100 Kg mass would pull on the rope with about a Kilonewton of force.

A Newton is just a different way of saying a force or weight of 1 kilogram times a meter divide by a second squared. (1 N = 1 kg x 1 m / 1 s^2)

A Mass of 1 Kilogram has a different weight depending on where you are exactly, but if you are on earth it usually is somewhere around 9.81 m / s^2 ( It can be as high as 9.83 m / s^2 and as low as 9.78 m / s^2).

If you don’t need super high accuracy using 10 m/s^2 for gravity on Earth is fine and you will err on the side of caution.

This gives you a nice round number like 10 Newtons of force per kilogram of mass.

So 1 Kilonewton is 1000 Newton which works out as the approximate force that a weight of 100 kg would produce here on earth due to gravity. (Really it would be 98.1 kg plus or minus a few hundred gram depending on location but 100 kg seems good enough.)

For traditional American units both force and mass are measured in pounds. This makes this one conversion easier but every other unit conversion more complicated and really messes things up when you need higher accuracy that takes into account that the relations between mass and weight is not the same everywhere)

You can get from Newtons measuring force to Pascal measuring pressure by dividing the force by the area and 1 Pascal is a newton divided by a square meter.

You can also get energy or work measured in Joule by multiplying Newton with a meter instead.

And you can get Power in Watt by multiplying it with a meter per second.