kg to Newtons Calculator converts a mass in kilograms to its weight in newtons at standard gravity, 9.80665 m/s², and turns newtons back into kg. A custom gravity value can be set.
A kilogram is mass and a newton is force, so gravity (g) is what links the two.
Gravity and Result Unit
Step-by-Step Working
- Known values: m = 5 kg, g = 9.80665 m/s²
- Formula: F = m × g
- Substitute: 5 × 9.80665
- Result: F = 49.0333 N
kg to Newtons Table
| Mass (kg) | Force (N) | Force (kN) |
|---|---|---|
| 1 | 9.80665 | 0.00980665 |
| 5 | 49.0333 | 0.0490333 |
| 10 | 98.0665 | 0.0980665 |
| 20 | 196.133 | 0.196133 |
| 30 | 294.2 | 0.2942 |
| 50 | 490.333 | 0.490333 |
| 70 | 686.466 | 0.686466 |
| 75 | 735.499 | 0.735499 |
| 100 | 980.665 | 0.980665 |
| 500 | 4,903.33 | 4.90333 |
| 1,000 | 9,806.65 | 9.80665 |
Why the kg to Newtons Calculator Needs g
A kilogram measures mass and a newton measures force, so one cannot simply be swapped for the other. The kg to Newtons Calculator joins them with gravity. It multiplies the mass by g and reports the weight, which is the force gravity puts on that mass.
The default g is standard gravity, exactly 9.80665 m/s². At that value 1 kg weighs 9.80665 N, and the opening entry of 5 kg comes out at 49.0333 N. The same number is the kilogram-force to newton factor in the NIST SP 811 conversion tables, which is why kg to N and kgf to N give identical answers.
Set Convert to Newtons to kg and the tool runs the other way. The accordion holds the gravity value and the result unit, so the same mass can be weighed on the Moon or at the poles and reported in kN or lbf. It belongs with the other Dynamics and Statics calculators, since weight is the force most problems start from.
kg to N Formula
To convert from kg to N, multiply the mass in kilograms by the acceleration of gravity in m/s². Weight is one case of force equals mass times acceleration, the general rule behind the Force Calculator.
$$F = m \times g$$
F is the weight in newtons, m is the mass in kilograms and g is gravity in meters per second squared. The Step-by-Step Working panel of the kg to Newtons Calculator sets the conversion out line by line. For 5 kg it reads as follows.
- Known values are m = 5 kg and g = 9.80665 m/s².
- The formula is F = m × g.
- Substituting gives 5 × 9.80665.
- The result is F = 49.0333 N.
There is an easy way to convert kg to N in your head. Multiply the kilograms by 10, then take off 2%. For 30 kg that is 300 minus 6, or 294 N, against an exact 294.2 N. The shortcut works because 9.80665 is about 2% below 10.
kg to Newtons Table
The table gives the values people look up most, all at standard gravity. The second column uses g = 9.81 m/s² because many textbooks do, and the last two columns restate the standard result in kilonewtons and pounds-force.
| Mass | Newtons at g = 9.80665 | Newtons at g = 9.81 | Kilonewtons | Pounds-force |
|---|---|---|---|---|
| 1 kg | 9.80665 N | 9.81 N | 0.00980665 kN | 2.20462 lbf |
| 5 kg | 49.0333 N | 49.05 N | 0.0490333 kN | 11.0231 lbf |
| 10 kg | 98.0665 N | 98.1 N | 0.0980665 kN | 22.0462 lbf |
| 20 kg | 196.133 N | 196.2 N | 0.196133 kN | 44.0925 lbf |
| 30 kg | 294.2 N | 294.3 N | 0.2942 kN | 66.1387 lbf |
| 50 kg | 490.333 N | 490.5 N | 0.490333 kN | 110.231 lbf |
| 70 kg | 686.466 N | 686.7 N | 0.686466 kN | 154.324 lbf |
| 75 kg | 735.499 N | 735.75 N | 0.735499 kN | 165.347 lbf |
| 100 kg | 980.665 N | 981 N | 0.980665 kN | 220.462 lbf |
| 500 kg | 4,903.33 N | 4,905 N | 4.90333 kN | 1,102.31 lbf |
| 1,000 kg | 9,806.65 N | 9,810 N | 9.80665 kN | 2,204.62 lbf |
A metric ton of 1,000 kg therefore weighs just under 10 kN. The kg to Newtons Calculator builds the same kind of table under its results. A mass that is not on the list is added as a highlighted row, and the whole table is recalculated if you change g.
Newtons to kg
To calculate from N to kg, divide the force in newtons by g. The answer is the mass whose weight on Earth equals that force. In the kg to Newtons Calculator this is the Newtons to kg setting of the Convert menu.
$$m = \frac{F}{g}$$
For 100 N the working is 100 ÷ 9.80665 = 10.1972 kg. The result can also be shown in grams, metric tons, pounds or ounces through the Result Unit menu. Forces entered in kilonewtons or pounds-force are converted to newtons first.
| Force | Mass in kilograms | Mass in grams |
|---|---|---|
| 1 N | 0.101972 kg | 101.972 g |
| 2 N | 0.203943 kg | 203.943 g |
| 5 N | 0.509858 kg | 509.858 g |
| 12 N | 1.22366 kg | 1,223.66 g |
| 50 N | 5.09858 kg | 5,098.58 g |
| 70 N | 7.13801 kg | 7,138.01 g |
| 100 N | 10.1972 kg | 10,197.2 g |
| 200 N | 20.3943 kg | 20,394.3 g |
| 1,500 N | 152.957 kg | 152,957 g |
One newton is the weight of about 102 g, so the common claim that 1 newton equals 100 grams is a rounding that runs 2% low. Five newtons is the weight of roughly half a kilogram, and 2 newtons is about 204 grams.
This division only makes sense when the force is a weight. A 100 N push on a cart tells you nothing about the cart’s mass until you know how fast it speeds up. In that case the link between newtons and kilograms is the acceleration, which the Acceleration Calculator works out from the net force and the mass.
Is 1 kg 9.8 N or 10 N?
Strictly, 1 kg is not equal to any number of newtons. What is true is that 1 kg weighs 9.80665 N under standard gravity. The figures 9.81, 9.8 and 10 are all roundings of that one value, and each appears in different textbooks.
The first card of the kg to Newtons Calculator shows what each rounding does to your entry. For 5 kg it gives 49.05 N with g = 9.81, 49 N with g = 9.8 and 50 N with g = 10. Against the standard value, 9.81 is 0.03% high, 9.8 is 0.07% low and 10 is 2% high.
People say 1 kg equals 10 newtons because 10 m/s² makes mental arithmetic simple, and a 2% error rarely matters in a rough estimate. For homework, use the g your textbook states, or the answer key will not match. For unit conversion and engineering work, use 9.80665.
The same reasoning answers the reverse question. One newton is not 1 kg. It is the weight of 0.101972 kg, so it takes almost ten newtons to hold up a single kilogram. Pressed on a kitchen scale, a force of one newton reads about 102 g.
Kilograms and Kilonewtons
One kilonewton is 1,000 newtons, which is the weight of 101.972 kg. A single kilogram is therefore nowhere near 1 kN. It weighs 0.00980665 kN, a little under one hundredth of a kilonewton.
The shop-floor rule that 1 kN is 100 kg is close but not exact. A 100 kg mass weighs 0.980665 kN, so the rule overstates the load by 2%. Kilonewtons are the usual unit once forces get large, such as the impact loads from the Car Crash Calculator.
What Is 1 Newton?
One newton is the force that gives a mass of 1 kg an acceleration of 1 m/s², so 1 N equals 1 kg·m/s². In other force units it is 0.101972 kgf, 0.224809 lbf or 100,000 dynes. The second card restates every result this way, and 5 kg reads 11.0231 lbf, 0.0490333 kN and 4.90333 × 10⁶ dyn.
US units keep the same split between mass and force. A mass of 1 lb weighs exactly 1 lbf at standard gravity, so 150 lb entered as the mass returns 667.233 N, which is 150 lbf. The third card adds the slug, the US mass unit of 14.5939 kg that pairs with pounds-force. Five kilograms is 0.342609 slug.
Weight Away from Standard Gravity
Standard gravity is an agreed reference, not the pull at any one place. NASA’s Earth Fact Sheet lists 9.780 m/s² at the equator and 9.832 m/s² at the poles. The fourth card applies both, and 5 kg weighs 48.9 N at the equator and 49.16 N at the poles. The gap of 0.26 N is about 0.5%.
The Gravity field takes any other value, in m/s² or ft/s², where standard gravity is about 32.174 ft/s². NASA’s Moon Fact Sheet gives the Moon’s surface gravity as 1.62 m/s². With that entered, 5 kg weighs only 8.1 N, and a 70 kg person weighs 113.4 N instead of 686.466 N.
The mass stays the same in every case, and only the newtons change. In physics problems that state their own g, the kg to Newtons Calculator follows that value and labels the answer as weight at your g. The Gravitational Force Calculator finds g for any planet from its mass and radius.
Weight in newtons is also the force a hanging load puts on a spring. The Hooke’s Law Calculator takes it from there and returns the stretch or the spring constant. A 5 kg load, for example, pulls on its spring with the 49.0333 N found above.
kg to Newton Meter and kg/m³
A newton meter is a unit of torque, so kilograms cannot become newton meters without a distance. Convert the mass to weight first, then multiply by the lever arm r measured from the pivot.
$$\tau = m \times g \times r$$
A 5 kg mass hanging 0.3 m from a pivot weighs 49.0333 N and produces 49.0333 × 0.3 = 14.71 N·m. For torque values already written in kilogram-force meters, the factor is the familiar one, and 1 kgf·m equals 9.80665 N·m.
Searches for a kg to newtons calculator with kg/m³ are about density, not mass. Multiplying a density by g gives specific weight, the weight of each cubic meter of material in N/m³.
$$\gamma = \rho \times g$$
Water at 1,000 kg/m³ has a specific weight of 9,806.65 N/m³, or 9.80665 kN/m³. Enter the density as the mass in the kg to Newtons Calculator and read the newtons as newtons per cubic meter, since the arithmetic is the same.