Force Calculator

Based on Newton's Second Law of Motion

Select which variable you want to calculate and input the other values.

Practical Examples

Load an example to see how the calculator works.

Calculate Force

force

Calculate the force needed to accelerate a 2kg object at 5 m/s².

Calculate: force, m=2kg, a=5m/s²

Calculate Mass

mass

Find the mass of an object if a force of 100N causes it to accelerate at 4 m/s².

Calculate: mass, F=100N, a=4m/s²

Calculate Acceleration

acceleration

Find the acceleration of a 50kg object when a force of 200N is applied.

Calculate: acceleration, F=200N, m=50kg

Gravitational Force on Earth

force

Calculate the gravitational force (weight) of a 70kg person on Earth.

Calculate: force, m=70kg, a=9.8m/s²

Other Titles
Understanding Force: A Comprehensive Guide
Explore the fundamental concepts of force, its calculation using Newton's laws, and its applications in the real world.

What is Force?

  • Defining Force in Physics
  • Vector Nature of Force
  • Units of Force
In physics, a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity.
Key Concepts
Force is a fundamental concept that explains why objects move the way they do. The study of forces is central to mechanics. The standard unit of force is the Newton (N). One Newton is defined as the force required to accelerate a one-kilogram mass at a rate of one meter per second squared (1 N = 1 kg·m/s²).

Examples of Forces in Daily Life

  • Pushing a shopping cart.
  • The Earth's gravity pulling you down.
  • A magnet attracting a paperclip.
  • Friction slowing down a sliding puck.

Step-by-Step Guide to Using the Force Calculator

  • Choosing the Calculation Type
  • Entering Input Values
  • Interpreting the Results
Our Force Calculator is designed to be simple and intuitive. It's based on Newton's Second Law of Motion, which states that Force equals Mass times Acceleration (F = m × a).
How to Calculate Force (F)
1. Select 'Force (F)' from the 'Variable to Calculate' dropdown menu. 2. Enter the mass of the object in kilograms (kg). 3. Enter the acceleration in meters per second squared (m/s²). 4. Click 'Calculate' to see the resulting force in Newtons (N).
How to Calculate Mass (m) or Acceleration (a)
The process is similar. Simply select 'Mass (m)' or 'Acceleration (a)' from the dropdown. The calculator will rearrange the formula to m = F / a or a = F / m, respectively. Fill in the two known values, and the calculator will find the unknown one.

Calculation Scenarios

  • To find the force for a 10 kg mass accelerating at 2 m/s², you'd input m=10 and a=2 to get F=20 N.
  • To find the mass of an object that accelerates at 3 m/s² under a 15 N force, you'd input F=15 and a=3 to get m=5 kg.

Real-World Applications of Force Calculations

  • Engineering and Construction
  • Automotive Design
  • Sports Science
The principles of force are not just confined to physics classrooms; they are integral to many fields of engineering, technology, and science.
Structural Engineering
Engineers must calculate the forces acting on bridges, buildings, and other structures to ensure they are safe and stable. This includes static forces like the weight of materials and dynamic forces like wind or earthquakes.
Vehicle Dynamics
Automotive engineers use force calculations to design cars with optimal performance, safety, and efficiency. They analyze forces such as engine thrust, air resistance, and friction to determine a car's acceleration and braking capabilities.

Application Examples

  • Calculating the thrust a rocket engine needs to overcome Earth's gravity.
  • Designing a braking system that can safely stop a high-speed train.
  • Analyzing the forces on a prosthetic limb to ensure it functions naturally.

Common Misconceptions and Correct Methods

  • Mass vs. Weight
  • Net Force vs. Individual Forces
  • Force and Motion
Mass is Not Weight
One of the most common misconceptions is confusing mass and weight. Mass is the amount of matter in an object and is constant everywhere (measured in kg). Weight is the force of gravity acting on that mass (W = m × g) and changes depending on the gravitational field (measured in N). An astronaut has the same mass on Earth and the Moon, but their weight is much less on the Moon.
Constant Force and Constant Velocity
Another point of confusion is the relationship between force and motion. Many believe that a constant force is needed to maintain constant velocity. In reality, a constant velocity (zero acceleration) means the net force is zero. A constant force produces constant acceleration, not constant velocity. The force of an engine is required to counteract opposing forces like friction and air resistance to maintain a constant speed.

Clarification

  • A 10kg object is always 10kg, but its weight on Earth is ~98 N, while on Mars it's ~37 N.
  • If a car is moving at a constant 60 mph, the net force on it is zero. The engine's forward force perfectly balances the forces of air resistance and friction.

Mathematical Derivation and Examples

  • Newton's Second Law Formula
  • Rearranging the Formula
  • Worked-Out Example
The Core Formula: F = m × a
The mathematical foundation for our calculator is Newton's Second Law of Motion. It provides a direct relationship between the net force applied to an object, the object's mass, and the acceleration it experiences. The formula is: F = m × a. Where: F is the net force in Newtons (N), m is the mass in kilograms (kg), and a is the acceleration in meters per second squared (m/s²).
Solving for Mass and Acceleration
Using simple algebra, we can rearrange the formula to solve for the other variables: To find mass (m), if you know the force (F) and acceleration (a), the formula is: m = F / a. To find acceleration (a), if you know the force (F) and mass (m), the formula is: a = F / m.

Worked-Out Example

  • Problem: A force of 50 N is applied to a 10 kg box. What is its acceleration?
  • Solution: Using a = F / m, we get a = 50 N / 10 kg = 5 m/s².