Newton's Second Law Calculator
This Newton's Second Law calculator solves F = ma for any unknown — force, mass, or acceleration. Choose what you want to find, enter the two known values, and pick your units for an instant answer in SI and common engineering units.
Enter known values
Select which quantity to solve for, then enter the other two.
F = ma: the three forms
F = m × a (force from mass and acceleration)
m = F ÷ a (mass from force and acceleration)
a = F ÷ m (acceleration from force and mass)
In SI: force in newtons (N), mass in kilograms (kg), acceleration in m/s². The standard gravity constant g = 9.80665 m/s² is used for weight calculations and g-force conversions.
Common Questions
Frequently asked questions
- What is Newton's Second Law?
- Newton's Second Law of Motion states that the net force acting on an object equals its mass multiplied by its acceleration: F = m × a. This is the cornerstone of classical mechanics — it tells you how much an object accelerates when a given force is applied, how much force is needed to achieve a target acceleration, or what mass is being pushed by a known force producing a known acceleration.
- What units does Newton's Second Law use?
- In SI units, force is in newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²). One newton is the force required to accelerate 1 kg at 1 m/s²: 1 N = 1 kg·m/s². In imperial units, force is in pounds-force (lbf) and mass in slugs (or pounds-mass with gravitational conversion). This calculator supports N, kN, lbf for force; kg, g, lb for mass; and m/s², g-force for acceleration.
- What is the relationship between weight and Newton's Second Law?
- Weight (W) is the gravitational force on an object: W = m × g, where g is the local gravitational acceleration (≈ 9.81 m/s² on Earth's surface). This is a direct application of Newton's Second Law — Earth's gravity exerts a force on a mass, and that force is what a scale measures. On the Moon (g ≈ 1.62 m/s²), the same 70 kg person weighs only about 113 N instead of 687 N.
- What is the difference between mass and weight?
- Mass is the amount of matter in an object (measured in kg) — it is the same everywhere in the universe. Weight is the gravitational force acting on that mass (measured in N or lbf) — it varies with the local gravitational field. An astronaut in orbit is weightless (zero net gravitational force felt) but has the same mass as on Earth.
- What is g-force?
- G-force (or g) expresses acceleration as a multiple of Earth's standard gravitational acceleration: 1 g = 9.80665 m/s². A fighter pilot pulling 9 g experiences an acceleration of 9 × 9.81 ≈ 88.3 m/s². A person standing still experiences 1 g due to Earth's gravity (the normal force from the floor). This calculator lets you enter acceleration in m/s² or in multiples of g.
- How do I calculate the braking force needed to stop a car?
- Use F = m × a. A 1500 kg car decelerating from 100 km/h to rest in 4 seconds has acceleration a = Δv ÷ t = (100 ÷ 3.6) ÷ 4 ≈ 6.94 m/s². The required braking force is F = 1500 × 6.94 ≈ 10,417 N ≈ 10.4 kN. Enter mass 1500 kg, acceleration 6.94 m/s², and solve for force to confirm.
- What are Newton's other two laws?
- Newton's First Law (the law of inertia) states that an object at rest stays at rest, and an object in motion continues at constant velocity, unless acted on by a net external force. Newton's Third Law states that for every action (force), there is an equal and opposite reaction. Together, all three laws form the foundation of classical mechanics.