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How It Works
The force equation F = m × a (Newton's second law) tells you how much force is needed to accelerate an object. The heavier the object or the faster you want it to speed up, the more force you need. You can rearrange the same equation to solve for mass or acceleration when the other two values are known.
The SI unit of force is the newton (N). Other common units include dyne (CGS), kilogram-force (kgf), pound-force (lbf), and kip (1,000 lbf). Use the Solve For dropdown above to pick which variable to calculate.
Example Problem
A 1,200 kg car accelerates from rest to 20 m/s in 10 seconds. What force is required?
- Calculate acceleration: a = (20 − 0) / 10 = 2 m/s²
- Apply the force equation: F = 1,200 kg × 2 m/s² = 2,400 N
A simpler example: a 5 kg object accelerates at 3 m/s². The force is 5 × 3 = 15 N.
When to Use Each Variable
- Solve for Force — when you know mass and acceleration, e.g., determining the thrust needed to accelerate a vehicle.
- Solve for Mass — when you know force and acceleration, e.g., finding the mass of an object from its motion under a known force.
- Solve for Acceleration — when you know force and mass, e.g., calculating how quickly a rocket speeds up given its thrust and mass.
Frequently Asked Questions
What is the force equation?
The force equation is F = m × a, also known as Newton's second law. It states that force equals an object's mass multiplied by its acceleration. For example, pushing a 10 kg cart with an acceleration of 2 m/s² requires 20 N of force.
What is the difference between mass and weight?
Mass measures the amount of matter in an object (in kilograms) and stays the same everywhere. Weight is the gravitational force acting on that mass (in newtons) and changes depending on where you are. On the Moon, your weight is about one-sixth of what it is on Earth, but your mass is unchanged.
How does increasing mass affect acceleration?
If the applied force stays the same, increasing the mass decreases the acceleration. This follows directly from a = F / m. Doubling the mass cuts the acceleration in half.
Can you use the force equation for objects moving in a circle?
Yes. For circular motion the centripetal force keeps the object on its curved path. You still apply F = m × a, where the acceleration is the centripetal acceleration directed toward the center of the circle.
What are common mistakes when using F = ma?
The most common errors are confusing mass with weight, using inconsistent units (e.g., grams instead of kilograms), and forgetting that force and acceleration are vectors with direction. Always convert to consistent units before calculating.
Related Calculators
- Gravity Equations Calculator — calculate gravitational force between two masses.
- Kinetic Energy Calculator — find the energy of a moving object from its mass and velocity.
- Newton's Second Law Calculator — explore additional forms and applications of F = ma.
- Impulse & Momentum Calculator — relate force, time, and momentum change.
- Friction Equations Calculator — calculate friction force from the normal force and coefficient.
- Force Unit Converter — convert between newtons, pounds-force, dynes, and more.
Reference: Tipler, Paul A. 1995. Physics For Scientists and Engineers. Worth Publishers. 3rd ed.