Force Calculator

Force is the push or pull that changes an object's motion. Isaac Newton quantified it: net force equals mass times acceleration. Engineers size structural members from anticipated loads, athletes feel force in every jump and tackle, and hydraulic systems translate pressure into linear force on pistons. The newton (N) — one kilogram accelerated at one m/s² — is the SI unit of force.

Newton's second law:

F = m × a

Where F is net force, m is mass, and a is acceleration. Impulse form from momentum change:

F = Δp / Δt = m(v − u) / t

Where Δp is momentum change, v and u are final and initial velocities, and t is contact or application time. Weight is a force: W = m × g with g ≈ 9.81 m/s².

Enter mass and acceleration for static or dynamic loading, or mass with initial/final velocity and time for impact-style estimates. Distinguish mass (kg) from weight (N). A 70 kg person weighs about 686 N on Earth but their mass stays 70 kg on the Moon where weight is only 114 N.

Worked example: A 0.15 kg baseball accelerates from 0 to 40 m/s in 0.008 s during a pitch. F = m(v−u)/t = 0.15 × 40 / 0.008 = 750 N — roughly the force to lift 75 kg. A 2,000 kg elevator accelerating upward at 1.5 m/s² needs cable tension T = m(g + a) = 2,000 × (9.81 + 1.5) ≈ 22,600 N including weight support.

Combine with the friction calculator for inclined planes and sliding contacts, the work calculator for force times distance, and the torque converter when rotational effects matter. Always resolve forces into components on angled surfaces before applying F = ma along each axis.