Force Calculator
Newton's Second Law of Motion is one of the most important relationships in classical physics: the net force (F) acting on an object equals its mass (m) multiplied by its acceleration (a). Written as F = m * a, this formula lets you solve for any one of the three variables when the other two are known. Force is measured in newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²). This calculator also computes the weight of an object using W = m * g, where g = 9.81 m/s² is the standard gravitational acceleration on Earth's surface as defined by the International Bureau of Weights and Measures (BIPM). Weight is a force and is therefore expressed in newtons, not kilograms. Select which variable you want to find, enter the two known values, and the result updates instantly. Common uses include physics homework, engineering design checks, and understanding everyday forces such as braking distance, structural loads, and athletic performance.
Result: -- N
Formula and explanation
Newton's Second Law relates three physical quantities:
F = m * a
m = F / a
a = F / m
W = m * g (g = 9.81 m/s² on Earth)
Worked example
A 5 kg box is pushed with an acceleration of 3 m/s². What is the net force?
- F = m * a
- F = 5 kg * 3 m/s²
- F = 15 N
Its weight on Earth: W = 5 * 9.81 = 49.05 N
SI units for force
| Quantity | Symbol | SI Unit | Unit Symbol |
|---|---|---|---|
| Force | F | Newton | N |
| Mass | m | Kilogram | kg |
| Acceleration | a | Metre per second squared | m/s² |
| Weight | W | Newton | N |
| Gravitational acceleration | g | 9.81 m/s² | m/s² |
Frequently asked questions
What is Newton's Second Law of Motion?
Newton's Second Law states that the net force acting on an object equals the product of its mass and its acceleration: F = m * a. Force is measured in newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²). If the net force is zero, the object either stays at rest or moves at constant velocity (Newton's First Law).
What is the difference between mass and weight?
Mass is the amount of matter in an object, measured in kilograms (kg). It does not change with location. Weight is the gravitational force acting on that mass: W = m * g, where g is the gravitational field strength. On Earth, g = 9.81 m/s², so a 10 kg object weighs 98.1 N. On the Moon (g = 1.62 m/s²), the same object weighs only 16.2 N, but its mass remains 10 kg.
What is a newton (N)?
The newton is the SI unit of force. One newton is defined as the force required to accelerate a mass of one kilogram at one metre per second squared: 1 N = 1 kg * m/s². It is named after Sir Isaac Newton. In everyday terms, a medium apple weighs approximately 1 N on Earth.
Can force be negative?
Yes. Force is a vector quantity, meaning it has both magnitude and direction. A negative force value in a one-dimensional problem simply means the force acts in the opposite direction to the chosen positive direction. For example, if rightward is positive, a leftward friction force would be negative. The magnitude of the force is always positive.
How is this formula used in real engineering?
F = ma is foundational to structural engineering, vehicle design, aerospace, and biomechanics. Engineers use it to calculate braking forces, structural loads, rocket thrust requirements, and the forces on bridge supports. Combined with other equations of motion, it underpins virtually all classical mechanics and mechanical design.
Sources
- NIST SP 330 (2019 edition): The International System of Units (SI).
- BIPM: SI Measurement Units.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. General information only.