Force Calculator — Newton's Second Law (F = m × a)
The Force Calculator lets you instantly find force, mass, or acceleration using Newton's Second Law of Motion: F = m × a. Choose any unknown variable, enter the two known values, and get the result in multiple unit systems — metric and US customary.
What is Force?
Force is any interaction that, if unopposed, can change the motion of an object. In classical mechanics, force is described by Newton's Second Law:
F = m × a
where F is force (Newtons), m is mass (kilograms), and a is acceleration (m/s²).
The greater the mass of an object or the greater its acceleration, the greater the force required. In SI units, one Newton (N) equals one kilogram-meter per second squared (1 N = 1 kg·m/s²).
Newton's Laws of Motion
- First Law (Inertia): An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by a net external force.
- Second Law (F = ma): The acceleration of an object is directly proportional to the net force and inversely proportional to its mass.
- Third Law (Action-Reaction): For every action there is an equal and opposite reaction.
Types of Forces
- Gravitational Force — the attraction between objects with mass (e.g., weight)
- Normal Force — the perpendicular force a surface exerts on an object
- Friction Force — the resistance force opposing relative motion
- Tension Force — the pulling force transmitted through a rope or cable
- Applied Force — any direct push or pull on an object
- Centripetal Force — the inward force required for circular motion
- Buoyancy Force — the upward force exerted by a fluid on an immersed object
How to Use the Force Calculator
- Select your unit system: Metric (SI) or US Customary (Imperial).
- Choose what to solve for: Force, Mass, or Acceleration.
- Enter the two known values with their respective units.
- Click Calculate to see the result with full unit conversions.
Metric vs US Customary Units
| Quantity | Metric (SI) | US Customary |
|---|---|---|
| Force | Newton (N), kN, MN, dyne | Pound-force (lbf), kip |
| Mass | Kilogram (kg), gram (g), tonne (t) | Pound (lb), ounce (oz), slug, short ton |
| Acceleration | m/s², cm/s² | ft/s², in/s² |
Force Formula Variations
- Find Force: F = m × a
- Find Mass: m = F ÷ a
- Find Acceleration: a = F ÷ m
Net Force
The net force is the vector sum of all forces acting on an object. If multiple forces act in the same direction, they add together. If they act in opposite directions, they partially cancel. The net force determines the actual acceleration via Newton's Second Law.
Example: A 70 kg person accelerating at 2 m/s²: F = 70 × 2 = 140 N.
Common Unit Conversions
- 1 N = 0.2248 lbf (pound-force)
- 1 N = 100,000 dyn (dynes)
- 1 kN = 1,000 N
- 1 lbf = 4.4482 N
- 1 kip = 1,000 lbf = 4,448.2 N
- 1 slug = 14.594 kg
- 1 kg·m/s² = 1 N