Force Calculator (F = ma)
Newton's second law defines the relationship between an object's mass, its acceleration, and the net force acting on it, three quantities that govern everything from car crashes to rocket launches.
Formula
Worked example
10 kg at 9.81 m/s² (gravity): F = 10 × 9.81 = 98.1 N (22.05 lbf), the object’s weight.
How the Calculator Works
The calculator applies Newton's second law of motion, which states that net force equals mass multiplied by acceleration. Mass is entered in kilograms (kg) and acceleration in metres per second squared (m/s²), and the result is expressed in newtons (N), the SI unit of force. One newton is defined as the force required to accelerate a one-kilogram mass at one metre per second squared, which follows directly from the base SI units.
How to Use It
Enter the mass of the object in kilograms and the magnitude of its acceleration in m/s². If you are working with deceleration, enter acceleration as a negative value to obtain a negative (opposing) force. The calculator returns the net force in newtons. For everyday reference, a 70 kg person standing on Earth experiences a gravitational force of roughly 686 N downward.
What Affects the Result
The result reflects net force only, the combined effect of all forces acting on the object along the direction of motion. Changing either mass or acceleration changes the force proportionally: doubling the mass doubles the force, and doubling the acceleration doubles it as well. The direction of the force vector matches the direction of acceleration, so the sign of your acceleration input matters for problems involving braking, deceleration, or opposing motion.
Limitations to Keep in Mind
This calculator assumes classical (Newtonian) mechanics and is not valid for objects moving at a significant fraction of the speed of light, where relativistic corrections become necessary. It also assumes the mass of the object remains constant during the motion, which excludes scenarios like rocket propulsion where mass changes over time. Additionally, the result represents net force, if you need to find one component force among several acting on a body, you will need to apply vector decomposition separately.
Solving for mass or acceleration (reverse mode)
Because F = m·a links three quantities, knowing any two lets you find the third. Switch the "Solve for" menu to Mass to compute m = F/a, the mass whose stated force and acceleration match, or to Acceleration to compute a = F/m, how fast a known force accelerates a given mass. The calculator converts every entry to SI units (kilograms, metres per second squared, newtons) before solving, so you can freely mix pounds, grams, g-force or pounds-force in the inputs and still get a correct answer. The result is shown in its natural SI unit, and for force we also report pounds-force and g-force for quick comparison.
Finding force from a velocity change
When you do not know the acceleration directly but you do know how the velocity changed, switch the acceleration source to "From a velocity change over time". The calculator first finds acceleration as the change in velocity divided by the time interval, a = (v_f − v_i)/t, then applies F = m·a. This is the form used for impacts, braking and launches: a 1000 kg car going from 27 m/s to 0 in 3 seconds undergoes about −9 m/s² and needs roughly 9000 N of braking force. Enter velocities in metres per second and time in seconds.
Everyday forces for comparison
| Situation | Approx. force | Notes |
|---|---|---|
| Weight of a 1 kg apple | 9.81 N | m × g at Earth’s surface |
| Weight of a 70 kg adult | 686 N | 70 × 9.81 |
| Hard bite (human jaw) | ~700 N | Molar bite force |
| Car braking (1000 kg, hard stop) | ~9000 N | F = m × deceleration |
| Rocket engine (Merlin, sea level) | ~845000 N | SpaceX Falcon 9 first stage |
Approximate magnitudes to sanity-check your result.
Frequently asked questions
What is a newton, and why is it the standard unit of force?
A newton (N) is the SI unit of force, defined as the force that gives a mass of one kilogram an acceleration of one metre per second squared. It is the standard unit because the SI system is coherent, using newtons, kilograms, and m/s² ensures that no conversion factors are needed when applying Newton's second law. The unit is named after Sir Isaac Newton in recognition of his formulation of the laws of motion.
Can I use this calculator for weight as well as force?
Yes. Weight is a force, specifically, the gravitational force acting on a mass. To find weight, enter the object's mass in kilograms and use 9.81 m/s² as the acceleration (standard gravitational acceleration at Earth's surface). The result in newtons is the object's weight. Note that weight varies slightly by location because gravitational acceleration differs between, for example, sea level and high altitude.
Does Newton's second law apply to rotational motion?
Newton's second law in its linear form (F = ma) applies to translational motion, straight-line or curvilinear movement of a point mass or the centre of mass of a rigid body. For rotational motion, the analogous relationship is the net torque equals the moment of inertia multiplied by angular acceleration. This calculator addresses only the linear case and does not account for rotational dynamics.
Can this calculator solve for mass or acceleration, not just force?
Yes. Use the "Solve for" menu to choose the unknown. Solving for force uses F = m·a, solving for mass uses m = F/a, and solving for acceleration uses a = F/m. The other two quantities become the inputs, and you can enter them in any of the offered units (kilograms, pounds, grams, newtons, pounds-force, m/s², g-force).
How do I find force from a speed change instead of acceleration?
Set the acceleration source to "From a velocity change over time" and enter the initial velocity, final velocity, and the time over which the change happens. The calculator computes acceleration as (v_f − v_i)/t and then multiplies by mass to give the force. A negative result means the force opposes the motion, as in braking.