What this calculator does
Find how hard something is being pushed, how heavy it is, or how fast it speeds up. You only need two of the three. The rule behind it is Newton's second law: F = ma. In words, the net force (F) equals mass (m) times acceleration (a). Acceleration is how quickly something speeds up or slows down. A bigger push gives a bigger acceleration. A heavier object needs more push to speed up at the same rate. One newton is the force that speeds up one kilogram by one meter per second, every second.
Pick the value you want, and the calculator works it out from the other two. For force it accepts newtons, kilonewtons or pounds-force. For mass it takes kilograms, grams, pounds or tonnes. For acceleration it takes meters or feet per second squared, or multiples of standard gravity (g, the pull of Earth's gravity). The working shows each unit conversion and the final formula, so you can follow along.
Where it's used
Why this math matters outside the classroom:
- Car acceleration. A 1,200 kg car accelerating at 2 m/s² needs a net force of 1,200 × 2 = 2,400 N from its tires.
- Finding mass. Students push a cart with 30 N, measure 1.5 m/s² and find its mass is 30 ÷ 1.5 = 20 kg.
- Crumple zones. Car safety engineers design crumple zones that slow a crash down, so the same change in speed needs a smaller force.
- Weight. Engineers convert a 75 kg mass into its weight on Earth, about 75 × 9.81 ≈ 736 N.
Grade level and standards: Grades 8–9; Common Core State Standards for Mathematics HSA.CED.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Choose whether to solve for force, mass or acceleration.
- Enter the two values you know, with their units. Force and acceleration can be negative to show direction.
- Choose the unit for the answer and read the result. It's also listed in the other units.
What the inputs mean
- Net force (F)
- This is the net force: all the pushes and pulls along the direction of motion, added together. For example, engine thrust minus friction and air drag.
- Mass (m)
- Mass is how much matter an object contains. It's always positive, and it's the same anywhere, unlike weight.
- Acceleration (a)
- 1 g is standard gravity, set at exactly 9.80665 m/s² by definition. People often describe the acceleration of cars, rides and aircraft in g.
Formula and method
F = m × a m = F ÷ a a = F ÷ m 1 lbf = 0.45359237 kg × 9.80665 m/s² = 4.4482216152605 N
F is the force, m is the mass and a is the acceleration. With mass in kilograms and acceleration in m/s² (meters per second, every second), force comes out in newtons (N). The calculator converts other units to these first. Then it converts the answer to the unit you choose.
A pound-force (lbf) is the weight of one pound of mass under standard gravity. That's why one pound sped up at 1 g gives exactly 1 lbf. To solve for mass, the acceleration can't be zero. It also has to point the same way as the force.
Worked example
A 1,200 kg car accelerates at 3 m/s². What net force is acting on it?
- F = m × a = 1200 × 3 = 3,600 N.
- In kilonewtons: 3600 ÷ 1000 = 3.6 kN.
- In pounds-force: 3600 ÷ 4.4482216 ≈ 809.31 lbf.
Result: The net force on the car is 3,600 N (3.6 kN, about 809 lbf).
Understanding the result
A negative result means the force or acceleration points the opposite way from the direction you called positive. Braking is a good example.
Weight is a special case, where the acceleration is gravity. A 1 kg mass weighs about 9.81 N on Earth.
Assumptions and limitations
- Mass is constant during the acceleration.
- Force and acceleration act along the same straight line.
- Speeds are far below the speed of light.
- It finds only the net force. Splitting it into thrust, friction or drag needs more information.
- Rockets and other things that lose mass as they move need a different form of the law.
- This version works along one straight line. A force at an angle must first be split into its parts along each direction (its components).
Frequently asked questions
What is a newton?
It's the metric (SI) unit of force. One newton speeds up a one-kilogram mass by one meter per second, every second. So 1 N = 1 kg·m/s². It's roughly the weight of a small apple.
What is the difference between pounds and pounds-force?
A pound (lb) is a unit of mass. A pound-force (lbf) is how hard standard gravity pulls on one pound of mass. On Earth the two numbers match for weight, but they measure different things.
How do I find the weight of an object?
Solve for force with the object's mass and an acceleration of 1 g. A 70 kg person weighs 70 × 9.80665 = 686.47 N, or about 154.3 lbf.
Why can't acceleration be zero when solving for mass?
With zero acceleration, the net force is zero for any mass. So there's no way to tell what the mass is. In the same way, a positive mass needs the force and acceleration to point the same direction.
How this calculator is checked
Method: Newton's second law of motion (F = ma); standard gravity 9.80665 m/s² (exact by definition). The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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