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Science

Newton's Second Law Calculator (F = m·a)

Enter any two of force F, mass m and acceleration a, and the tool back-solves the third. All values are SI (newtons N, kilograms kg, m/s²); mass is always > 0, while force and acceleration can be negative to indicate direction. Useful for high-school / AP physics, estimating vehicle braking force, sizing elevator and crane loads, comparing rocket thrust to weight, sports impact estimates, and more. The widget also shows the object's resting weight on Earth (W = m·g) so you can sanity-check the magnitudes.

Net force F

Derived

Mass m

Derived

Acceleration a

Derived

Formula

F = m · a | m = F / a | a = F / m

All values in SI units (newtons N, kilograms kg, metres per second squared m/s²). Mass is always > 0; force and acceleration can be negative to indicate direction.

Formula

F = m · a (solve for force) m = F / a (solve for mass; requires a ≠ 0) a = F / m (solve for acceleration) Reference: W = m · g, with g = 9.80665 m/s²

Frequently asked

Why does "F = 0 and a ≠ 0" give no answer when solving for mass?

Such a combination violates Newton's law itself: if the net force really is zero, the object must be at rest or moving at constant velocity (acceleration = 0). Dividing zero by a non-zero number gives 0, but a mass of 0 is physically meaningless (no inertia at all), so the tool refuses it. In practice this usually means you forgot a counter-force — friction, drag, the normal component on an incline, etc. — recompute the true net force first.

How do I convert kgf, lbf or g-force into N and m/s²?

Force conversions: 1 kgf (kilogram-force) ≈ 9.80665 N, 1 lbf (pound-force) ≈ 4.4482 N, 1 dyne = 1e-5 N. Acceleration conversions: 1 g (standard gravity) = 9.80665 m/s², so a 4 g cornering load = 39.227 m/s², a 9 g fighter manoeuvre ≈ 88.26 m/s²; 1 km/h/s ≈ 0.2778 m/s², 1 mph/s ≈ 0.4470 m/s². Convert first, then enter — the tool returns SI results.

How is F = ma different from W = mg, and does this tool give both?

W = m·g is just a special case of F = m·a — replace "net force" with "the gravity acting on a stationary object on Earth's surface" and set acceleration to g = 9.80665 m/s². Weight is mass × g. This tool uses the general F = m·a (any acceleration) and additionally shows W = m·g in the result strip, so you can quickly compare gravity vs. net force — e.g. inside an elevator accelerating upward, the cable tension is m·(g + a), which exceeds m·g.

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