Newton's Second Law Force: formula
Enter mass in kilograms and net acceleration in m/s². Force is mass times acceleration, and the result also converts newtons to pounds-force. The default 9.81 is a rounded example, not the exact standard-gravity constant of 9.80665 m/s².
Local gravity can differ.
Newton's Second Law Force: worked example
| Mass (kg) | 70 |
|---|---|
| Acceleration (m/s²) | 9.8 |
| Force (newtons) | 686.7 |
| Force (pounds-force) | 154.4 |
Mass is not weight: mass stays the same on the Moon while weight changes. Real problems have friction, drag and other forces, and the net force is the vector sum. The formula holds for constant mass at speeds well below light.
Pounds-force differs from pounds-mass.
Newton's Second Law Force: changing Mass (kg)
| Mass (kg) | Force (newtons) | Force (pounds-force) |
|---|---|---|
| 56 | 549.4 | 123.5 |
| 63 | 618 | 138.9 |
| 70 (example) | 686.7 | 154.4 |
| 77 | 755.4 | 169.8 |
| 84 | 824 | 185.3 |
Newton's Second Law Force: compare input ranges
| Input | Tested from | To | Force (newtons): low input | Force (newtons): high input | Swing |
|---|---|---|---|---|---|
| Acceleration (m/s²) | 9 | 11 | 630 | 770 | 140 (20%) |
| Mass (kg) | 63 | 77 | 618 | 755.4 | 137.3 (20%) |
Newton's Second Law Force: individual input comparisons
| Input | Value | Force (newtons) | Force (pounds-force) |
|---|---|---|---|
| Mass (kg) | 56 | 549.4 | 123.5 |
| 63 | 618 | 138.9 | |
| 70 | 686.7 | 154.4 | |
| 77 | 755.4 | 169.8 | |
| 84 | 824 | 185.3 | |
| Acceleration (m/s²) | 8 | 560 | 125.9 |
| 9 | 630 | 141.6 | |
| 10 | 700 | 157.4 | |
| 11 | 770 | 173.1 | |
| 12 | 840 | 188.8 |
Newton's Second Law Force: combined input changes
| Mass (kg) / Acceleration (m/s²) | 8 | 10 | 12 |
|---|---|---|---|
| 56 | 448 | 560 | 672 |
| 63 | 504 | 630 | 756 |
| 70 | 560 | 700 | 840 |
| 77 | 616 | 770 | 924 |
| 84 | 672 | 840 | 1,008 |
Newton's Second Law Force: which assumptions move the result?
Newton's Second Law Force: values and definitions
| Quantity and definition | Value used |
|---|---|
| Mass (kg) | 70 |
| Acceleration (m/s²) — 9.81 is a rounded example; defined standard gravity is 9.80665 m/s². | 9.8 |
| Force (newtons) | 686.7 |
| Force (pounds-force) | 154.4 |
Newton's Second Law Force: half and double Acceleration (m/s²)
| Acceleration (m/s²) | Force (newtons) |
|---|---|
| 4.9 | 343.4 |
| 9.8 | 686.7 |
| 19.6 | 1,373.4 |
Common error: Mixing up mass and weight. Weight is the force gravity puts on a mass, so the number of kilograms on a scale and the newtons of force are not the same quantity.
Physics & Mechanics calculators: Uniform Acceleration Calculator, Hooke's Law Calculator, Ideal Gas Law Calculator, Gravitational Potential Energy Calculator, Work and Power Calculator, Wavelength and Frequency Calculator.
Newton's second law ties force, mass and acceleration into one product. A 70 kilogram person under standard gravity, 9.81 meters per second squared, presses down with about 687 newtons, or roughly 154 pounds-force. The same formula sizes the pull needed to speed up a cart, the load on a lifting rope or the thrust a motor must provide.
Keep the units in step: kilograms, meters and seconds give newtons. Pounds of mass with feet per second squared gives a different unit entirely.
Find the energy on the kinetic energy calculator, the work on the work and power calculator and the spring force on the Hooke's law calculator. The centripetal force and free fall pages cover motion in a curve and falling, and the weight converter changes units.
What is Newton's second law?
The net force on an object equals its mass times its acceleration, so the same push accelerates a light object more than a heavy one.
What is the difference between mass and weight?
Mass is the amount of matter and does not change, while weight is the force of gravity on it, so it changes with location.
How many pounds-force are in a newton?
One newton is about 0.2248 pounds-force, and one pound-force is 4.448 newtons.