Introduction
Force is a push or pull that causes an object to speed up, slow down, or change direction. Newton's second law of motion tells us that force equals mass times acceleration (F = m × a). This simple equation connects three key values in physics, and if you know any two of them, you can solve for the third.
This force calculator lets you quickly find force, mass, or acceleration using Newton's second law. Enter two known values, pick your units, and the tool calculates the result. You can also calculate weight, which is the force of gravity acting on an object (F = m × g). The calculator supports many unit options, including newtons, pounds-force, kilograms, slugs, and several acceleration units. It shows your answer in multiple units at once and walks you through each step of the calculation so you can check your work or learn how the formula is applied.
This tool makes it easy to work through homework problems, check a design, or find out how much force a car or rocket produces. Choose from built-in examples like a falling object, a baseball pitch, or a rocket launch to see the formula in action with real-world numbers.
How to use our Force Calculator
Enter any two known values from Newton's second law of motion, and this calculator will find the missing third value. You can solve for force, mass, or acceleration, or calculate the weight of an object using gravity.
Calculation Mode: Choose what you want to solve for: Force (F = m × a), Mass (m = F / a), Acceleration (a = F / m), or Weight (F = m × g). The calculator will gray out the field it needs to solve and let you fill in the other two.
Force: Enter the force value if you already know it. Pick a unit from the dropdown, such as Newtons (N), kilonewtons (kN), pounds-force (lbf), or dynes (dyn). This field is left empty when you are solving for force.
Mass: Enter the mass of the object. You can choose from units like kilograms (kg), grams (g), pounds (lb), metric tons (t), or slugs. The default value is set to 1,000 kg as a starting point.
Acceleration: Enter how fast the object is speeding up or slowing down. Choose a unit such as meters per second squared (m/s²), feet per second squared (ft/s²), or g-forces. When calculating weight, this field is automatically set to Earth's gravity (9.80665 m/s²).
Quick Examples: Select a preset scenario from the dropdown to auto-fill realistic values. Options include a car going from 0 to 60 mph, an object falling on Earth, a rocket launch, a baseball pitch, and more.
Precision: Choose how many significant figures you want in your answer. The default is 5 figures, but you can pick anywhere from 3 to 12 or leave it on Auto.
Notation: Pick how you want numbers displayed: Standard, Scientific (like 2.5e3), or Engineering notation (exponents in multiples of three).
Unit System: Switch between SI (Metric), Imperial, or Mixed units. Changing this setting will update all three unit dropdowns at once to match your chosen system.
Calculate Button: Press this button to run the math. The results section will show your answer, the same value converted into every available unit, and a step-by-step breakdown of how the calculation was done.
Related Calculations: After getting your result, you can quickly find related values like Impulse (force × time), Work (force × distance), or Power (force × velocity) by clicking the buttons in the results section.
Understanding Force in Physics
Force is a push or pull that acts on an object. It can make something start moving, stop moving, speed up, slow down, or change direction. You cannot see force directly, but you can see what it does. When you kick a ball, your foot applies a force. When gravity pulls you down a slide, that is also a force. Force is one of the most important ideas in physics.
Newton's Second Law of Motion: F = m × a
The force calculator above is based on Newton's Second Law of Motion. This law says that force equals mass times acceleration, written as F = m × a. Mass is how much matter is in an object, measured in kilograms (kg). Acceleration is how quickly an object's speed changes, measured in meters per second squared (m/s²). Force is measured in newtons (N), named after Sir Isaac Newton, who first described these laws in 1687.
Here is what this means in plain terms: the heavier an object is, the more force you need to move it. And the faster you want it to speed up, the more force you need as well. A shopping cart that is full of groceries takes more force to push than an empty one. That is Newton's Second Law in action.
How the Three Variables Are Connected
Because force, mass, and acceleration are connected by one equation, you can rearrange it to solve for any of the three:
- Force: F = m × a. Multiply mass by acceleration to find force.
- Mass: m = F ÷ a. Divide force by acceleration to find mass.
- Acceleration: a = F ÷ m. Divide force by mass to find acceleration, a calculation you can also run on our Acceleration Calculator.
If you know any two of these values, you can always find the third. This is exactly what the calculator above does for you.
What Is Weight?
Weight is a special type of force. It is the force that gravity pulls on an object. On Earth, gravity accelerates everything at about 9.81 m/s². So the weight formula is W = m × g, where g is the acceleration due to gravity. A person with a mass of 70 kg has a weight of about 686 N on Earth. On the Moon, where gravity is weaker (about 1.62 m/s²), that same person would weigh only about 113 N. Their mass stays the same, but their weight changes because gravity is different.
Common Units of Force
The standard unit of force in the metric system is the newton (N). One newton is the force needed to accelerate a 1 kg object at 1 m/s². Other common units include:
- Kilonewton (kN): 1,000 newtons. Used in engineering for large forces like bridge loads.
- Pound-force (lbf): The standard force unit in the imperial system. One lbf equals about 4.448 N.
- Dyne (dyn): A very small unit used in the CGS system. One newton equals 100,000 dynes.
- Kilogram-force (kgf): The force of gravity on one kilogram. One kgf equals about 9.807 N.
Real-World Examples of Force
Force shows up everywhere in daily life and in engineering. Here are a few examples to give you a sense of scale:
- Picking up an apple: An apple weighs about 1 N.
- A baseball pitch: A pitcher applies roughly 50 N of force to throw a 95 mph fastball.
- Car acceleration: A 1,500 kg car speeding up at 2.68 m/s² (0 to 60 mph in 10 seconds) requires about 4,020 N of force.
- Rocket launch: The Saturn V rocket produced about 35 million N of thrust at liftoff.
- Elevator ride: A 1,000 kg elevator accelerating at 1.2 m/s² needs 1,200 N of net force beyond its weight.
Related Concepts
Force connects to many other ideas in mechanics. Work is force multiplied by distance (W = F × d), measured in joules. Impulse is force multiplied by time (J = F × Δt), measured in newton-seconds, and our Impulse Calculator works it out directly. Power is force multiplied by velocity (P = F × v), measured in watts. Understanding force gives you the foundation to explore all of these topics and solve real-world physics problems with confidence.