About the Force Calculator
Force problems are the backbone of introductory mechanics. Whether a question asks how hard a rocket engine pushes, how much a backpack weighs on the Moon, or how much friction stops a sliding box, the same few relationships do the work.
This calculator covers the three you meet first: Newton's second law for the net force, the weight of an object in a gravitational field, and the friction force between two surfaces. Every quantity in each formula can be the unknown, and all values use SI units, so newtons, kilograms and metres per second squared.
What is a force?
A force is a push or a pull that can change an object's motion. It has a size, measured in newtons, and a direction, so it is a vector. One newton is the force that gives a one-kilogram mass an acceleration of one metre per second squared, which is roughly the weight of a small apple.
When several forces act at once, what matters for the motion is their vector sum, the net force. If the net force is zero the object keeps moving at a constant velocity or stays at rest (Newton's first law); if it is not zero the object accelerates in the direction of the net force.
How to use the Force Calculator
- Choose F = ma, W = mg or f = μN.
- Type the values you know in SI units.
- Leave exactly one box empty: that is the unknown.
- For weight, leave g empty to use 9.81 m/s².
- Press Calculate force and read the rearranged formula and check.
Formulas
Newton's second law
Weight
Friction
Newton
Inclined plane (normal force)
Worked example: F = ma with m = 2 kg, a = 3 m/s²
A 800 kg car is pushed forward by a net force of 1200 N. Rearranging F = ma for the acceleration gives .
Check: N, the force we started with. After 4 seconds from rest the car would be moving at m/s, which you can explore further in the kinematics calculator.
The solution below is generated by the same engine that powers the calculator above.
Final answer
net force F = 6 N
How we read your problem
Use the Newton's second law formula, rearranged for the unknown, in SI units.
Step-by-step solution
Formula: Newton's second law
Substitute the known values
Formulas used
Newton's second law
Newton's second law links the net force on an object to its acceleration: F = ma. Force and acceleration point the same way, so a negative force gives a negative acceleration. One newton accelerates one kilogram by 1 m/s².
Verification
- Substituted every value back into the formula: both sides agree ✓
Detailed explanation
Using Newton's second law
F = ma uses the net force, not any single force. If a 10 kg crate is pulled with 50 N while friction pulls back with 20 N, the net force is 30 N and the acceleration is 3 m/s². Using 50 N would overstate the acceleration because it ignores the resisting force.
Signs carry direction in one-dimensional problems. Choose a positive direction, and enter forces and accelerations that point the other way as negative numbers. A braking force of −6000 N on a 1500 kg car gives a = −4 m/s²: the car slows down.
Mass versus weight
Mass measures how much matter an object contains and how strongly it resists changes in motion; it is the same everywhere. Weight is the gravitational force on that mass, W = mg, and depends on where you are. A 70 kg astronaut weighs about 687 N on Earth but only about 113 N on the Moon, where g is 1.62 m/s².
If you know both the weight and the mass, the calculator can find g instead. A 10 kg mass that weighs 16.2 N gives g = 1.62 m/s², the Moon's surface gravity.
Friction and the normal force
Friction depends on how hard two surfaces are pressed together, measured by the normal force N, and on the materials, captured by the coefficient μ. Kinetic friction on a sliding object is f = μₖN. Static friction adjusts to whatever is needed to prevent sliding, up to a maximum of μₛN.
On a level floor with no other vertical forces the normal force equals the weight, so a 20 kg box has N ≈ 196 N. On a ramp of angle θ it is smaller, mg cos θ, which is why objects slide more easily on steep slopes. Typical coefficients range from about 0.05 for ice to 0.8 for rubber on dry concrete.
Common mistakes
- Using one applied force instead of the net force in F = ma.
- Entering grams instead of kilograms.
- Confusing mass (kg) with weight (N).
- Using N = mg on a ramp or when someone pushes down on the object.
- Dropping the minus sign on a force that opposes the motion.
Tips
- Draw a free-body diagram before writing any equation.
- Pick a positive direction and keep it for the whole problem.
- Convert every value to SI units first.
- Check the units: kg times m/s² must give newtons.
- Use the projectile motion calculator once you know the acceleration.
Frequently asked questions
How do I calculate force?
Multiply mass in kilograms by acceleration in m/s²: F = ma. A 2 kg object accelerating at 3 m/s² needs a net force of 6 N.
How do I find acceleration from force and mass?
Divide the net force by the mass: a = F/m. Leave the acceleration box empty and the calculator does this for you.
What is the difference between mass and weight?
Mass is the amount of matter, in kilograms, and is the same everywhere. Weight is the gravitational force mg, in newtons, and changes with g.
What value of g should I use?
Near Earth's surface use 9.81 m/s² (some courses use 9.8 or 10). On the Moon g is about 1.62 m/s² and on Mars about 3.71 m/s².
What is the coefficient of friction?
A unitless number μ describing how grippy two surfaces are; friction equals μ times the normal force. It is usually between 0 and 1.
Can force be negative?
In one dimension a negative force simply points in the negative direction you chose. Its magnitude is still positive.
Why is the normal force not always equal to the weight?
On a slope, in an accelerating elevator, or when another force pushes up or down, the normal force adjusts and differs from mg.
Solve a force problem
Choose a formula above, enter what you know and leave the unknown empty.