A 12 kg cart accelerating at 2.5 m/s²
F = m × a
12 × 2.5 = 30 N. This is the net force. If friction is 10 N in the opposite direction, a forward push of 40 N would be needed for that net force.
Newton's second law
Force Calculator
Find net force, mass, or acceleration from the other two values. Mix units and keep direction with positive or negative signs.
Calculate force, mass, or acceleration
Net force
Enter the two known values, then select Calculate.
- Net force in newtons
- Mass in kilograms
- Acceleration in m/s²
- Formula
- Direction
Calculation steps
≈ marks display rounding. Calculations run in your browser. Press Enter to calculate. Successful results appear in this tab's Recent calculations.
Three worked examples
A −60 N net force on a 20 kg object
a = F ÷ m
−60 ÷ 20 = −3 m/s². The acceleration points along the negative axis. Its sign alone does not tell you whether the object is speeding up or slowing down.
A −10 lbf force producing −1 g₀
m = F ÷ a
The two negative signs cancel, giving 10 lb of mass, or 4.5359237 kg. Selecting g₀ converts an acceleration; it does not add a gravity force.
Model, units, and rounding
This tool applies F = ma to one axis in an inertial reference frame, with constant positive mass. It uses the net external force. It does not resolve vectors or add gravity, friction, drag, or other forces for you. Variable-mass systems and relativistic motion require a different model. See OpenStax — Newton's second law.
Unit conversions use exact definitions: 1 N = 1 kg·m/s², 1 kN = 1,000 N, 1 kg = 1,000 g, 1 lb = 0.45359237 kg, and 1 ft = 0.3048 m. Conventional standard gravity is 1 g₀ = 9.80665 m/s², so 1 lbf = 4.4482216152605 N. g₀ is a fixed unit, not a measurement of local gravity. References: NIST conversion factors and NIST exact pound and pound-force factors, notes 22–23.
The mass mode accepts nonzero force and acceleration with matching signs. Two zeros describe many possible positive masses, so they cannot determine a unique answer. Just one zero is inconsistent with a finite positive mass; opposite signs would imply a negative mass. Each of these cases receives an explanation instead of a numerical result.
Active inputs accept at most 64 characters, 15 integer digits, and 10 decimal places. Expressions, scientific notation, and units inside numeric fields are not accepted. Hidden fields are disabled and ignored. Force and acceleration may be zero when mass is supplied.
Arithmetic and unit conversions retain exact fractions. Only the displayed values are rounded; halfway values round away from zero, and trailing zeros are omitted. ≈ identifies rounding. A very small nonzero result may display as ≈ 0, with a notice explaining how to show more detail. Changing result units or decimal places updates the answer without adding a recent-calculation entry. Extra digits do not establish measurement accuracy.
Common questions
Is this the force of a push or the net force?
It is the net force along the selected axis. If several forces act, combine their signed components first. The force of one push equals the net force only when the other forces on that axis cancel or are absent.
Can force or acceleration be negative?
Yes. Their signs represent direction. With positive mass, force and acceleration have the same sign. A mass result remains positive when you divide a negative force by a negative acceleration.
Does zero net force mean the object is stopped?
No. Zero net force gives zero acceleration in this model. An object can remain at rest or continue moving at a constant velocity.
Why does 1 lb at 1 ft/s² not give 1 lbf?
The lb input is a mass unit. A pound-force is defined using standard gravity, about 32.174 ft/s², rather than an acceleration of 1 ft/s². The calculator uses the exact SI conversion factors so no additional conversion constant is needed in your input.
Can this calculate collision or impact force?
Only if you already have an appropriate net acceleration for the model. Mass and speed alone cannot determine an impact force. Contact time, deformation, and how the acceleration changes matter; this calculator does not model a collision or determine structural safety.