Newton's second law calculator
Force, mass or acceleration from F = m · a.
Fill in the fields and the result will appear here automatically.
Relates the magnitude of net external force, positive constant mass and acceleration magnitude using F = ma. Enter the resultant force after accounting for directions, rather than adding the magnitudes of opposing forces. This page does not solve directions. The additional weight row is mg at conventional standard gravity, 9.80665 m/s²; it is not a measurement of local gravity or an accelerating lift’s scale reading.
How it works
Formula and logic
For constant mass in an inertial frame: F = ma, m = F/a and a = F/m. F and a here are non-negative magnitudes of consistently directed vectors. Reference weight W = mgₙ uses gₙ = 9.80665 m/s²; it is not the net force when other forces balance gravity.
Example
A 10 kg mass accelerating at 2 m/s² has net force 20 N and reference weight 98.0665 N. A 30 N pull opposed by 10 N friction gives a resultant input of 20 N, not 40 N.
Fields and units
- What to find — list option
- Mass — kg
- Acceleration magnitude — m/s²
- Net force magnitude — N
- Acceleration magnitude — m/s²
- Net force magnitude — N
- Mass — kg
How to use
- — Choose force, mass or acceleration.
- — Use kg, N and m/s²; resolve directions before entering the resultant magnitude.
- — When finding mass, both supplied magnitudes must be positive; F = a = 0 does not determine mass.
- — Zero acceleration is valid when finding force, and zero net force is valid when finding acceleration of a positive mass.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: net force and Newton’s second law NIST: conventional standard gravity, 9.80665 m/s²
- Limitation
- Classical constant positive-mass model using resultant magnitudes; individual forces and their directions are not inferred.
FAQ
How does force differ from weight?
Force is a general quantity. F here is the net-force magnitude; the reference weight row is mgₙ. At rest, a support can balance weight, giving F = 0 despite non-zero mgₙ.
Why is zero acceleration rejected when solving for mass?
If F = a = 0, any positive mass fits. F > 0 with a = 0 contradicts this finite constant-mass model; division by zero cannot determine mass.
Can acceleration be zero when solving for force?
Yes: for m > 0 it gives F = 0. But F = 0 with non-zero a cannot yield a positive mass in the inverse mode.
Is friction taken into account?
Not automatically. Include friction, thrust and other external forces in their vector sum before entering the resultant magnitude.
Is standard gravity the exact gravity at my location?
No. 9.80665 m/s² is a conventional standard. Local gravity varies, and support-force readings also depend on the frame’s acceleration.