Newton's second law calculator: F = m × a
Solve Newton's second law in all three directions. Enter two values among net force, mass and acceleration, select units and calculate the third with SI conversion and worked equations.
Enter exactly two values among net force, mass and acceleration. Leave the quantity you want to calculate empty.
The calculator uses the scalar form of Newton's second law and positive magnitudes. For directional problems, apply the vector relationship component by component.
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How does this tool work?
This calculator applies Newton's second law, one of the central relationships in classical mechanics. The net external force on a system equals its mass multiplied by its acceleration. In scalar form the equation is F = ma. The tool solves for net force, mass or acceleration from the other two values, converts units automatically and shows the equation used.
The precise statement involves net force: F_net = ma. OpenStax explains that the net external force is the vector sum of the external forces acting on the system. If several forces act at once, their resultant must be determined before using this simple calculator.
When mass and acceleration are known, net force is F = ma. A 10 kg object accelerating at 2 m/s² has a net force of 20 N. If force and mass are known, acceleration is a = F/m. If force and acceleration are known, mass is m = F/a.
Calculations use coherent SI units internally: newtons for force, kilograms for mass and metres per second squared for acceleration. One newton is the force required to accelerate a 1 kg mass at 1 m/s², so 1 N = 1 kg·m/s².
Inputs can still use convenient units. Force may be entered in N, kN or lbf; mass in mg, g, kg, tonnes, ounces or pounds; and acceleration in m/s² or ft/s². The shared conversion engine converts everything to SI and then returns the result in the chosen display unit.
Mass and weight are not the same quantity. Mass measures inertia and is expressed in kilograms. Weight is a gravitational force and is expressed in newtons. Near Earth, W = mg is a particular application involving gravitational acceleration, not a replacement for the general second law.
Newton's second law is vectorial in full form: acceleration points in the same direction as net force. This calculator handles positive magnitudes for straightforward one-dimensional problems. In multiple dimensions, solve each component separately, such as ΣF_x = ma_x and ΣF_y = ma_y.
How to use this tool
Identify the net force
If several external forces act on the system, combine them vectorially before applying F = ma.
Enter two known quantities
Fill two fields among F, m and a and leave only the unknown quantity empty.
Select the measurement units
Each field can use a different supported unit; Bethemesh converts them to N, kg and m/s².
Review the working
The calculation section shows the rearranged equation, SI substitution and final value in your selected unit.
Newton's second law formulas
Net external force, mass and acceleration are linked by three equivalent scalar forms.
Net force
F = m × a
Net external force equals mass multiplied by acceleration.
Acceleration
a = F ÷ m
Acceleration equals net force divided by mass.
Mass
m = F ÷ a
Mass equals net force divided by acceleration.
Definition of the newton
1 N = 1 kg × 1 m/s²
The newton is the SI unit of force.
- F
- net external force, usually in newtons
- m
- mass of the system, usually in kilograms
- a
- acceleration of the system, usually in m/s²
The complete law is vectorial: net force and acceleration point in the same direction. This calculator uses positive magnitudes only.
Use cases
Mechanics exercises
Check Newton's second law, algebraic rearrangement and unit conversion in physics problems.
Study the effect of a force
Find the acceleration produced by a known net force on a given mass.
Estimate required net force
Calculate the theoretical resultant force required for a target acceleration before adding a detailed force model.
Infer mass from dynamics
Determine mass from measured acceleration and known net force in a simple mechanical model.
Examples
Calculate net force
F = ma = 10 × 2 = 20 N.
Input
m = 10 kg; a = 2 m/s²Result
F = 20 NCalculate acceleration
a = F/m = 600/1200 = 0.5 m/s².
Input
F = 600 N; m = 1200 kgResult
a = 0.5 m/s²Find mass
2 kN = 2000 N, so m = 2000/4 = 500 kg.
Input
F = 2 kN; a = 4 m/s²Result
m = 500 kgMass entered in grams
250 g = 0.25 kg; F = 0.25 × 8 = 2 N.
Input
m = 250 g; a = 8 m/s²Result
F = 2 NImperial inputs
The values are converted through SI units and returned in ft/s².
Input
F = 100 lbf; m = 50 lbResult
a ≈ 64.35 ft/s²Tips and best practices
- Use net force, not an arbitrary single force, when several forces act on the object.
- Do not confuse kilograms and newtons: kilograms measure mass, newtons measure force.
- If acceleration is zero, the net force is zero even though individual nonzero forces may cancel.
- For motion in more than one direction, apply Newton's law separately to each coordinate component.
- Include friction, drag, tension and support forces whenever they contribute to the resultant force.
- Keep extra digits during conversions and round only the final value.
Sources and references
- OpenStax, 4.3 Newton's Second Law of Motion (opens in a new tab), PhysicsPage in English
- BIPM — SI Brochure: units of time (opens in a new tab)Page in English
Frequently asked questions
What is Newton's second law formula?
In scalar form, F_net = ma: net external force equals mass multiplied by acceleration.
How do I calculate force from mass and acceleration?
Multiply mass by acceleration: F = ma. A 5 kg mass accelerating at 3 m/s² requires a net force of 15 N.
How do I calculate acceleration?
Divide net force by mass: a = F/m.
How do I calculate mass?
Divide net force by acceleration: m = F/a.
What is a newton?
One newton is the force that accelerates 1 kg at 1 m/s², so 1 N = 1 kg·m/s².
Are force and weight the same?
Weight is a particular gravitational force. Mass is a different property and is measured in kilograms.
Why does the formula use net force?
Several forces can act simultaneously. Newton's second law applies to their vector sum, the net external force.
Can acceleration be negative?
Yes in a signed or vector problem. This calculator uses positive magnitudes; direction or sign should be applied according to the coordinate axis you define.
Are my values sent to a server?
No. Unit conversion and calculation run locally in your browser.
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