Calculate force, mass or acceleration using Newton's second law (F=ma)
Force is the fundamental interaction that causes objects to accelerate, as described by Newton's Second Law of Motion: F = ma (Force equals mass times acceleration). In SI units, 1 Newton (N) is the force required to accelerate a 1 kg mass at 1 m/s². Force is a vector — it has both magnitude and direction. The four fundamental forces of physics are gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. In everyday engineering, we work primarily with gravitational force (weight = mg), applied forces, normal forces, friction, tension, and spring forces.
This calculator solves Newton's Second Law for any unknown: force (given mass and acceleration), mass (given force and acceleration), or acceleration (given force and mass). It also calculates weight from mass (using g = 9.80665 m/s²), converts between force units (N, kN, lbf, kgf, dyne), and handles net force from multiple force components.
Mass is the amount of matter in an object — it's a scalar, measured in kilograms (kg), and doesn't change based on location. Weight is the gravitational force on an object: W = mg. On Earth's surface, g ≈ 9.81 m/s². On the Moon, g ≈ 1.62 m/s² — so a 70 kg person has the same mass everywhere but weighs 686 N on Earth and only 113 N on the Moon. In everyday speech "weight" is often used loosely to mean "mass" — but in physics, they are distinct.
Newton (N): SI unit, 1 N = 1 kg⋅m/s². Kilonewton (kN): 1000 N. Pound-force (lbf): force of gravity on 1 pound mass at standard g, 1 lbf ≈ 4.448 N. Kilogram-force (kgf or kp): force of gravity on 1 kg, 1 kgf = 9.80665 N. Dyne: CGS unit, 1 dyne = 10⁻⁵ N. Ton-force (tf): 1 tf = 9806.65 N ≈ 9.81 kN.
Static friction prevents an object at rest from starting to move: Fs ≤ μs × N (where μs is static friction coefficient, N is normal force). Kinetic (sliding) friction acts on a moving object: Fk = μk × N. Static friction coefficient is always higher than kinetic: μs > μk, which is why it takes more force to start moving an object than to keep it moving. Typical values: rubber on dry concrete μs ≈ 0.6–0.8, steel on steel μs ≈ 0.4–0.6.
Net force is the vector sum of all forces acting on an object. Newton's Second Law applies to net force: a = Fnet/m. If net force is zero, acceleration is zero (object at rest or moving at constant velocity — Newton's First Law). Example: a 100 N rightward push and 40 N leftward friction on a 10 kg box: Fnet = 100 - 40 = 60 N rightward; a = 60/10 = 6 m/s² rightward.
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