EngineeringFormulaEngineering Mechanics
Force Calculator
Solve net force, mass, or acceleration using Newton's second law in scalar form: F = m a.
Newton's second law relates net force, mass, and acceleration: F = m a. This calculator lets you solve for any one of the three when the other two are known. It uses the one-dimensional scalar form of the equation, so force and acceleration may be entered as signed values along a chosen axis, while mass must remain positive.
m · Mass of the object or system being accelerated.
a · Acceleration of the object or system along the chosen axis.
Scalar sign convention: mass stays positive. Force and acceleration may be positive or negative if you are working along a single chosen axis.
Solution
Enter the required values to calculate net force.
F = m a
Formula Sheet
- FNet Force
- mMass
- aAcceleration
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| F | Net Force | Resultant external force acting along the chosen axis. | N, kN, lbf |
| m | Mass | Mass of the object or system being accelerated. | g, kg, lb |
| a | Acceleration | Acceleration of the object or system along the chosen axis. | m/s², ft/s², g |
How to Use This Calculator
- 01Choose which variable to solve for - Force, Mass, or Acceleration - using the solve-for selector.
- 02Enter the other two known values and select the unit for each field. Mass must be positive; force and acceleration can be positive or negative if you are using a one-dimensional sign convention.
- 03Select Calculate to see the answer in base SI units, plus a secondary unit conversion where useful.
- 04If you solve for mass, force and acceleration must have the same sign in a scalar 1D setup; otherwise the implied mass would be non-physical and the calculator will flag it.
- 05If your problem has several pushes, pulls, friction forces, or angled forces, first combine them into one signed net force using a free-body diagram or the Net Force Calculator, then use that net force here.
How the Formula Works
Newton's second law states that the net external force on a system equals its mass multiplied by its acceleration: F = m a. For a fixed mass, force and acceleration are directly proportional - doubling the force doubles the acceleration. For a fixed force, acceleration is inversely proportional to mass, so a heavier system accelerates less under the same applied net force.
This calculator uses the scalar form of the law, which is appropriate when all motion is analyzed along one chosen axis. In that format, force and acceleration can carry signs to indicate direction. A negative force simply means the net force points opposite the positive axis you selected.
Worked Example 01
Solving for force
Known
- Mass (m): 10 kg
- Acceleration (a): 3 m/s²
Formula
F = m a
Substitution
F = 10 × 3
Result
F = 30 N
A 10 kg system accelerating at 3 m/s² requires a net force of 30 N along the chosen axis.
Worked Example 02
Solving for mass
Known
- Net Force (F): 30 N
- Acceleration (a): 3 m/s²
Formula
m = F / a
Substitution
m = 30 / 3
Result
m = 10 kg
If a 30 N net force produces 3 m/s² of acceleration, the mass is 10 kg.
Worked Example 03
Solving for acceleration with a negative force
Known
- Net Force (F): -20 N
- Mass (m): 8 kg
Formula
a = F / m
Substitution
a = -20 / 8
Result
a = -2.5 m/s²
The negative sign indicates acceleration opposite the positive axis chosen for the problem.
Applications
- 01Newton's second law homework and exam problems
- 02Estimating acceleration from a known net force and mass
- 03Checking the net force required to accelerate a mechanical system
Assumptions
- 01The equation is applied in one-dimensional scalar form along a chosen axis.
- 02The force entered is the net external force, not just one individual force among several.
- 03Mass is treated as constant during the motion.
Where This Model Stops
- 01Does not resolve multiple forces into a vector resultant; use a dedicated net-force or force-components calculator for multi-direction force systems.
- 02Not suitable for variable-mass systems such as rockets during fuel burn without a more complete momentum analysis.
- 03Does not include friction, drag, rolling resistance, spring force, or impact duration automatically; those must be calculated separately and included in the net force if relevant.
- 04The scalar sign tells direction along one chosen axis only. It is not a full 2D or 3D vector result.
References
- [1]4.3 Newton's Second Law of Motion
OpenStax Physics
Defines the relationship between net force, mass, and acceleration as F_net = m a.
- [2]Force Equals Mass Times Acceleration: Newton's Second Law
NASA
Applies Newton's second law in an engineering and aerospace learning context.
Frequently Asked Questions
Is this force or net force?
This is net force. Newton's second law uses the resultant external force acting on the system, not just one individual applied force unless that applied force is already the net force.
Can force and acceleration be negative?
Yes in a one-dimensional sign convention. A negative value means the quantity points opposite the positive axis you chose. Mass, however, must remain positive.
Why can this calculator not handle multiple angled forces?
Because this version uses the scalar form F = ma. Multi-force or multi-direction problems require vector addition first, then Newton's second law can be applied to the resultant.
How is this different from the Net Force Calculator?
The Net Force Calculator combines multiple forces into one resultant. This Force Calculator applies Newton's second law once you already know the resultant force, mass, or acceleration.