π Newton's Second Law Calculator
Solve F = ma for force, mass, or acceleration.
Force
How to Use This Calculator
Select the unknown, enter the other two quantities with units, and the calculator solves F = ma with automatic conversions across metric and imperial systems.
Choose Force, Mass, or Acceleration.
Enter the known values and pick units (kg, lb, slugs; m/sΒ², ft/sΒ², g).
Read the answer plus conversions and g-force equivalents.
The Formula
Force and acceleration are vectors pointing the same way. The equation also reads as a definition of the newton: one newton accelerates one kilogram at one m/sΒ². Friction, tension, normal force, and thrust all plug into the same equation as components of the net force.
Worked Example
A 70 kg person standing on Earth: F = 70 Γ 9.81 = 686.7 N of weight. To accelerate a 1,200 kg car at 3 m/sΒ² needs F = 3,600 N of net force, before accounting for drag and rolling resistance.
Why It Matters
From designing elevators (apparent weight changes with acceleration) to sizing rocket engines, F = ma turns desired motion into required force. Crash safety engineers use it in reverse: given a survivable deceleration, they compute the stopping distance airbags and crumple zones must provide.
Common Mistakes to Avoid
F = ma uses NET force: subtract friction and other opposing forces first. Grams must become kilograms (divide by 1,000) before multiplying by m/sΒ². A 'g' of acceleration is 9.81 m/sΒ², so 3 g is 29.4 m/sΒ², not 3. Weight in pounds-force is already a force; do not multiply by g again. For rotating systems, the linear form does not apply directly; use torque and moment of inertia instead.
F = ma in Engineering and Safety
Crash safety is applied F = ma. A 70 kg occupant stopping from 50 km/h in 0.1 seconds experiences average forces near 10 kN, but stretching the stop to 0.5 seconds with crumple zones and airbags cuts that to about 2 kN. Every safety system in a car is fundamentally a device for lowering acceleration during the inevitable momentum change.
Engineers use the same law in reverse to size motors, brakes, and structures. Elevator cables, bridge supports, and rocket engines are all specified by the forces they must exert or withstand under known accelerations. Remember that the law is vectorial: only the net force along each axis counts, so friction and opposing forces must be subtracted before solving for the resulting acceleration.
Frequently Asked Questions
What is Newton's second law?
F = ma: the net force on an object equals its mass times its acceleration. It is the workhorse of classical mechanics, predicting how objects respond to pushes and pulls.
What is net force?
Net force is the vector sum of all forces acting on an object. Opposing forces cancel; only the net force causes acceleration. A book resting on a table has zero net force despite gravity pulling down.
What units are used?
SI: newtons (N) = kgΒ·m/sΒ² for force, kg for mass, m/sΒ² for acceleration. Imperial: pound-force (lbf), slugs, ft/sΒ². This calculator converts between both systems.
How is weight related to F = ma?
Weight is the gravitational force on a mass: W = mg with g = 9.81 m/sΒ² on Earth. Your mass is the same on the Moon, but your weight is one-sixth because g is smaller.
What is a g-force?
G-force expresses acceleration as a multiple of Earth's gravity. A 3 g turn means you feel three times your weight. Fighter pilots and astronauts train to withstand high g without blacking out.