F = ma Calculator
Solve Newton's second law in any direction — enter any two of force (N), mass (kg), and acceleration (m/s²) to calculate the third, with a worked example.
How this is calculated
Newton's second law relates force, mass and acceleration with a single equation, F = ma. Rearranged, that gives m = F / a (solving for mass) or a = F / m (solving for acceleration) — whichever field you leave blank determines which form of the equation is used.
All three rearrangements, with worked examples: to find force, F = ma — a 1,200 kg car accelerating at 3 m/s² needs F = 1,200 × 3 = 3,600 N. To find mass, m = F / a — if a 3,600 N force produces 3 m/s² of acceleration, the mass is m = 3,600 / 3 = 1,200 kg. To find acceleration, a = F / m — that same 3,600 N force applied to a 1,200 kg car produces a = 3,600 / 1,200 = 3 m/s². For a related physics calculation involving motion under gravity, see the Projectile Motion calculator, and for the analogous relationship between voltage, current, and resistance in electrical circuits, see the Ohm's Law calculator.
A common exam and real-world problem: "A force of 350 N causes a body to accelerate at 10 m/s² — find the mass." Using m = F / a: m = 350 / 10 = 35 kg. The reverse: "A 35 kg trolley accelerates at 10 m/s² — what force is applied?" F = 35 × 10 = 350 N. Both follow from the same equation; the calculator handles all three forms — just leave the unknown field blank. Another example: a rocket exerts 15,000 N of thrust on a 750 kg stage, giving a = 15,000 / 750 = 20 m/s². On the Moon, the same thrust with 1/6 of Earth's gravity means apparent weight is lower, but the thrust-driven acceleration is identical — mass does not change with gravity, only weight does.
Frequently asked questions
- What is Newton's second law?
- It states that force equals mass times acceleration (F = ma) — the net force acting on an object determines how quickly its velocity changes, in proportion to its mass. It's one of the three foundational laws of classical mechanics.
- What units does this use?
- Force in newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²) — the standard SI units.
- Why do I only fill in two fields?
- Because the formula only has three variables and one equation relating them — once you know any two, the third is fully determined. Leave whichever one you want calculated blank.
- Can I use this in my own app?
- Yes — every calculator on Stupidly Clever has a matching REST API and MCP tool that runs the same underlying logic.
- How do I calculate acceleration if force and mass are known?
- Rearrange F = ma to solve for acceleration: a = F / m. Enter the force and mass values and leave acceleration blank to have this calculator do it for you.
- What is the SI unit of force?
- The newton (N), defined as the force needed to accelerate a 1 kg mass at 1 m/s². One newton is a relatively small force — roughly the weight of a small apple resting in your hand.
- What is the difference between mass and weight?
- Mass is the amount of matter in an object, measured in kilograms, and does not change regardless of location. Weight is the force gravity exerts on that mass (weight = mass × gravitational acceleration), measured in newtons, and varies depending on the local gravitational field — the same object weighs less on the Moon despite having identical mass.
- What is the formula for F = ma?
- F = ma means Force (in newtons) equals Mass (in kilograms) multiplied by Acceleration (in metres per second squared). Rearranged: m = F / a to find mass, or a = F / m to find acceleration. This calculator handles all three rearrangements — leave whichever variable you want to find blank.
- How do I calculate force from mass and acceleration?
- Multiply mass by acceleration: F = m × a. For example, a 70 kg person accelerating at 9.8 m/s² (free fall under gravity) experiences a force of 70 × 9.8 = 686 N — equivalent to their weight in newtons. Enter 70 in the mass field and 9.8 in acceleration and leave force blank to confirm.
- A force of 350 N causes a body to move with an acceleration of 10 m/s² — what is the mass?
- Rearrange F = ma to m = F / a: m = 350 / 10 = 35 kg. Enter 350 in the force field, 10 in acceleration, and leave mass blank — the calculator gives 35 kg directly. This is one of the most common rearrangement problems: whenever you know force and acceleration, mass is simply the ratio.
- What is the net force on a 1,500 kg car accelerating at 2.5 m/s²?
- F = ma = 1,500 × 2.5 = 3,750 N. This is the net force — the engine force minus friction and air resistance combined. The calculator solves this in one step: enter 1500 for mass and 2.5 for acceleration.
- Can acceleration be negative, and what does that mean?
- Yes — negative acceleration (deceleration) means the object is slowing down in the positive direction, or speeding up in the negative direction. The formula still holds: F = ma with a negative acceleration gives a negative (opposing) force. For example, brakes applying −5 m/s² to a 1,000 kg car produce a braking force of −5,000 N.