Force Calculator (F = ma)
Solve Newton's second law F = ma for force, mass, or acceleration. Enter any two of the three values and get the third with step-by-step working shown.
Newton's second law
Newton's second law of motion says the net force on an object equals its mass times its acceleration:
- F — force, in newtons (N)
- m — mass, in kilograms (kg) — always positive
- a — acceleration, in metres per second squared (m/s²) — can be negative
Enter any two values and leave the third blank; the calculator solves for it and shows the substitution step.
Worked example
A 10 kg object accelerates at 2 m/s². What net force acts on it?
- Formula: F = ma
- Substitute: F = 10 × 2
- Result: F = 20 N
Solving in reverse
The same formula rearranges to find mass or acceleration when force is known:
- Mass: m = F / a — enter F and a, leave m blank.
- Acceleration: a = F / m — enter F and m, leave a blank.
For example, a 20 N force on a 10 kg object gives a = 20 / 10 = 2 m/s².
Common mix-ups
- Confusing mass and weight. Mass (kg) is how much matter an object has; weight (N) is the force of gravity on that mass — see the weight calculator for W = mg.
- Inconsistent units. Mixing pounds, grams, or ft/s² with SI values gives a wrong answer — convert everything to kg, m/s², and N first.
- Forgetting the sign. Deceleration is just a negative acceleration in this formula, not a special case.
Where this shows up
F = ma underlies almost all of classical mechanics: it explains why heavier objects need more force to accelerate at the same rate, why braking distance depends on mass, and why a small push barely moves a truck but easily moves a bicycle. Related quantities built on the same law include momentum (p = mv) and pressure (P = F/A).
Frequently asked questions
- What is the formula for force?
- Newton's second law: F = ma, where F is force in newtons (N), m is mass in kilograms (kg), and a is acceleration in metres per second squared (m/s²).
- How do I find mass if I know force and acceleration?
- Rearrange the formula to m = F / a. Enter the force and acceleration values and leave the mass field blank, and the calculator solves it for you automatically.
- Can the acceleration or force be negative?
- Yes. A negative acceleration means the object is slowing down or accelerating in the opposite direction to the one you called positive, and force then comes out negative too — only mass must be a positive number.
- What units does this calculator use?
- SI units throughout — newtons (N) for force, kilograms (kg) for mass, and metres per second squared (m/s²) for acceleration. Convert other units (pounds, grams, ft/s²) to SI before entering them.
- Why can't I leave two fields blank?
- The calculator solves for exactly one unknown from the other two known values. With two blanks there are infinitely many (m, a) pairs that give the same F, so leave only the single variable you want solved blank.
- How is force different from weight?
- Weight is a specific case of F = ma where the acceleration is gravity (g ≈ 9.8 m/s²). Force is the general relationship between mass and any acceleration — see the weight calculator for the gravity-specific version.