What is Newton's Second Law?

Newton's Second Law states that the net force acting on an object equals its mass multiplied by its acceleration: F = ma. Force is measured in Newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s2). A force of 1 Newton accelerates a mass of 1 kg at 1 m/s2.

What is the difference between mass and weight?

Mass is the amount of matter in an object, measured in kilograms, and does not change with location. Weight is the gravitational force acting on that mass, measured in Newtons: W = mg, where g is gravitational acceleration (9.81 m/s2 on Earth). A 10 kg object has a weight of 98.1 N on Earth but only about 16.2 N on the Moon.

How many Newtons are in a kilogram-force?

One kilogram-force (kgf) equals 9.80665 Newtons, which is the weight of one kilogram of mass under standard gravity. Kilogram-force is a deprecated unit still used in some engineering and everyday contexts, such as cable tension and hydraulic pressure ratings.

Force Calculator (F = ma)

This calculator applies Newton's Second Law of Motion, F = ma, to solve for any one of the three variables when you know the other two. Force is the product of an object's mass and its acceleration, measured in Newtons (N). One Newton is the force required to accelerate one kilogram of mass at one metre per second squared. When you select Solve for Force, you enter mass in kilograms and acceleration in m/s squared, and the calculator returns the force in Newtons, kilonewtons, and kilogram-force for reference. When you select Solve for Mass, you enter force in Newtons and acceleration in m/s squared, and the calculator tells you the mass in kilograms and tonnes. When you select Solve for Acceleration, you enter force in Newtons and mass in kilograms, and the calculator returns the acceleration in m/s squared. A common use is finding the weight force of an object: set the acceleration to g = 9.81 m/s squared and the mass to your object's mass to get its weight in Newtons. This tool is useful for physics students, mechanical engineers sizing motors and actuators, and anyone working through dynamics problems. The formula applies to the net force on a rigid body in a single direction; it does not account for friction, drag, or multiple forces acting simultaneously.

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Solve for

Mass (m)

Acceleration (a)

m/s²

Force (F)

98.10 N

force

Kilonewtons0.098 kN

Kilogram-force10.00 kgf

How it works

The three rearrangements of Newton's Second Law are: F = ma (force), m = F / a (mass), and a = F / m (acceleration). Select the variable you want to find, enter the other two, and the calculator applies the appropriate formula. Kilonewtons are Newtons divided by 1,000. Kilogram-force (kgf) are Newtons divided by 9.80665, representing the weight of one kilogram at standard gravity.

Worked example

A 10 kg object accelerates at 9.81 m/s² (the acceleration due to gravity). Force = 10 × 9.81 = 98.10 N. In kilonewtons that is 0.098 kN. In kilogram-force that is 98.10 / 9.80665 = 10.00 kgf, confirming that a 10 kg object has a weight of 10 kgf. These match the defaults above.

Related calculators

Acceleration Calculator: solve a = (v - u) / t for the acceleration term used here.
Kinetic Energy Calculator: find the energy stored in a moving object.
Potential Energy Calculator: gravitational PE = mgh.
Free Fall Calculator: apply F = mg to a falling object.

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