Force Calculator (F = ma)
Solve for force, mass, or acceleration using Newton's second law F = m × a. Enter any two values and choose the units for each field.
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About Newton's Second Law
Newton's second law of motion describes how force, mass, and acceleration relate to one another:
F = m × a
- F — force, measured in newtons (N)
- m — mass, measured in kilograms (kg)
- a — acceleration, measured in metres per second squared (m/s²)
In plain language: the force needed to accelerate an object is proportional to both how much matter it has (its mass) and how quickly you want its velocity to change (its acceleration). Double the mass and you need twice the force to produce the same acceleration. Double the acceleration and you likewise need twice the force. Rearranging the formula gives the other two forms used by this calculator:
- m = F / a — mass from force and acceleration
- a = F / m — acceleration from force and mass
Mass vs. Weight
This is one of the most common points of confusion in physics, so it's worth spelling out clearly. Mass (measured in kilograms) is a measure of how much matter an object contains. It is an intrinsic property of the object and does not change no matter where the object is located — on Earth, on the Moon, or floating in deep space.
Weight, on the other hand, is a force — specifically, the force of gravity acting on that mass. Weight is calculated using the very same equation this calculator solves: weight = mass × gravitational acceleration. On Earth's surface, gravitational acceleration is approximately 9.80665 m/s² (also written as "1 g"), so a 70 kg person weighs about 70 × 9.80665 ≈ 686.5 newtons.
Because weight depends on local gravitational acceleration, it does change with location, even though mass stays exactly the same. The Moon's gravitational acceleration is only about 1.62 m/s² — roughly one-sixth of Earth's — so an object's weight on the Moon is about 1/6 of its weight on Earth, even though its mass is completely unchanged. A 70 kg astronaut is still 70 kg on the Moon; they just weigh far less there.
To find your own weight in newtons using this calculator, select Force as the variable to solve for, enter your mass in kilograms, set acceleration to 1 g (9.80665 m/s²), and click Calculate. The "Standing still under gravity" quick example above does exactly this for a 70 kg person.
How to Use This Calculator
- Select which variable you want to solve for — Force, Mass, or Acceleration — using the tabs at the top.
- Enter values for the other two variables in their respective fields.
- Choose the appropriate units for each input using the dropdowns.
- Click Calculate — or try one of the quick example buttons to pre-fill common real-world scenarios.
Results are shown together in SI units (newtons, kilograms, and m/s²), with the force result also converted into pound-force (lbf) and kilogram-force (kgf) for convenience. Once you know an object's acceleration, the Speed and Velocity Calculator can help find how fast it will be moving after a given time.
Common Forces and Accelerations
| Scenario | Approx. mass | Approx. acceleration | Resulting force |
|---|---|---|---|
| Person standing on Earth | 70 kg | 9.80665 m/s² (1 g) | ~686.5 N |
| Car braking hard | 1,500 kg | 8 m/s² | ~12,000 N |
| Rocket at launch | 2,800,000 kg | ~2.7 m/s² | ~7,600,000 N |
| Pushing a shopping cart | 25 kg | 2 m/s² | 50 N |
| Fighter jet pilot (high-g turn) | 80 kg | ~88 m/s² (9 g) | ~7,050 N |
Unit Conversion Reference
| Quantity | Unit | Equivalent in SI base unit |
|---|---|---|
| Force | 1 kN | 1,000 N |
| Force | 1 lbf | 4.4482216153 N |
| Force | 1 kgf | 9.80665 N |
| Force | 1 dyne | 0.00001 N |
| Mass | 1 lb | 0.45359237 kg |
| Mass | 1 slug | 14.5939 kg |
| Acceleration | 1 g (standard gravity) | 9.80665 m/s² |
| Acceleration | 1 ft/s² | 0.3048 m/s² |
Newton's second law sits alongside other foundational formulas in this site's science-tools collection — including the Ideal Gas Law Calculator for relating pressure, volume, and temperature of a gas.
Frequently Asked Questions
What is a newton?
A newton (N) is the SI unit of force, named after Sir Isaac Newton, who formulated the laws of motion. One newton is defined as the force required to accelerate a 1 kg mass at a rate of 1 m/s². It's a relatively small unit in everyday terms — an average apple resting on your hand exerts roughly 1 N of force due to gravity.
What's the difference between mass and weight?
Mass is the amount of matter in an object, measured in kilograms, and it never changes regardless of location. Weight is the force gravity exerts on that mass, measured in newtons, and it changes depending on the local gravitational acceleration — for example, your weight on the Moon is about one-sixth of your weight on Earth even though your mass is identical in both places. See the "Mass vs. Weight" section above for the full explanation and how to calculate it here.
What does "g-force" mean in everyday contexts?
"G-force" expresses acceleration as a multiple of standard gravity (1 g = 9.80665 m/s²) rather than in raw m/s² or ft/s² units. It's commonly used for roller coasters, fighter jet maneuvers, and crash tests because it gives an intuitive sense of how many "times your own body weight" you'd feel — a 3 g turn feels three times as forceful as normal gravity. This calculator lets you enter acceleration directly in g using the unit dropdown.
Why would acceleration ever be negative?
Force and acceleration are technically vector quantities — they have both a magnitude and a direction. When an object slows down (like a car braking), its acceleration points opposite to its motion, which is often written as a negative number relative to a chosen direction of travel. This calculator works with the magnitude of acceleration (how strongly it's slowing down or speeding up), so for a braking scenario you'd simply enter the deceleration's magnitude, such as 8 m/s², rather than -8.
How does this relate to kinetic energy?
Force and acceleration determine how an object's velocity changes over time, and any object that gains velocity due to an applied force also gains kinetic energy. Once you've worked out the force or acceleration involved in a scenario here, the Kinetic Energy Calculator can help you find how much energy that object has once it reaches a given speed.
