Newton’s Second Law — F = m·a — is the single most useful equation in classical mechanics. It links three fundamental quantities: the net force acting on an object (in newtons), its mass (in kilograms), and the acceleration that results (in metres per second squared). This calculator extends that core relationship across six practical modes so you can handle the most common A-level and university physics problems from one place: solving for any one of F, m, or a; computing impulse and momentum change; finding work, power, and kinetic-energy change; resolving friction on a flat surface; calculating the centripetal force for circular motion; and decomposing forces on an inclined plane. Step-by-step working is shown for every calculation and can be copied with a single click.
How it works
F = ma mode — enter any two of force, mass, and acceleration; choose which to solve for. The calculator also reports the weight (m·g, with g = 9.81 m/s²) and, for acceleration, the result as a multiple of g.
Impulse mode uses the impulse-momentum theorem: J = F·Δt = Δp = m·(v_f − v_i). Fill the force+time block, the momentum block, or both. The tool reports impulse J, initial and final momenta, and the momentum change. If both blocks are filled it cross-checks F·Δt against Δp.
Work and Power mode applies W = F·d·cos θ. When you add the elapsed time t the tool also reports average power P = W/t. Supply mass and velocities to invoke the work-energy theorem (ΔKE = ½m·v_f² − ½m·v_i²) and verify it matches W.
Friction mode computes f = μ·N where N = m·g on a horizontal surface. Add an applied force at a downward angle θ and the calculator adjusts N = m·g + F·sin θ, then finds the net horizontal force and resulting acceleration.
Circular motion mode evaluates F_c = m·v²/r, which is Newton’s Second Law applied to the inward (centripetal) acceleration a_c = v²/r. Period T = 2πr/v and angular velocity ω = v/r are also reported.
Inclined plane mode resolves weight into the component perpendicular to the slope (N = m·g·cos θ) and the component parallel to it (m·g·sin θ). Optional kinetic friction (f = μ·N) is subtracted or added depending on whether the object moves down or up the slope. The net force divided by mass gives the acceleration.
Worked example
A 10 kg box is pushed across a floor with a 60 N horizontal force. The coefficient of kinetic friction is 0.25.
- Normal force — on a flat surface N = m·g = 10 × 9.81 = 98.1 N
- Friction — f = μ·N = 0.25 × 98.1 = 24.525 N
- Net force — F_net = 60 − 24.525 = 35.475 N
- Acceleration — a = F_net / m = 35.475 / 10 = 3.548 m/s²
Select the Friction tab, enter m = 10, μ = 0.25, applied force = 60 N at 0°, and the calculator shows all four values with working in one step.
Formula note
All six modes use g = 9.81 m/s² (standard gravity). The calculator assumes a flat Earth (no variation with altitude), constant mass (non-relativistic speeds), and that the given force is the net force (sum of all forces) unless the friction or inclined-plane mode separates the individual components. For problems involving multiple forces, find the resultant first before entering it here.