Newton's Second Law Calculator F = ma: Force in Newtons

About this calculator

Newton's second law connects net force, mass and acceleration:

F=ma.

Enter mass and acceleration to calculate net force, or provide force with one of the other variables to solve for the missing quantity. In SI units, force is measured in newtons, where $1\,N=1\,kg\cdot m/s^2$ .

The formula uses net force, the vector sum of all forces acting on the object. A single applied force is equal to $ma$ only when other forces are either absent or already included in the net.

Formula and variables

F=ma,\qquad a=\frac{F}{m},\qquad m=\frac{F}{a}

Symbol	Meaning	SI unit	Notes
$F$	net force	N	signed in a one-dimensional setup
$m$	mass	kg	positive scalar
$a$	acceleration	m/s²	signed along the chosen axis

Weight near Earth's surface is a force $W=mg$ . The standard acceleration of gravity is $g_0=9.80665\,m/s^2$ ; values such as 9.8 or 9.81 are common rounded approximations.

How to use this calculator

Enter mass in kilograms and acceleration in meters per second squared to compute net force in newtons.
To solve for acceleration, clear acceleration and enter force plus mass.
To solve for mass, clear mass and enter force plus acceleration.
Use signs consistently if treating the problem as one-dimensional.
Distinguish mass in kilograms from weight in newtons.

Worked examples

Example 1: 10 kg object accelerating at 3 m/s²

Example 2: a 1,500 kg car under 4,500 N net force

Example 3: weight of an 80 kg person

Using $g=9.80665\,m/s^2$ ,

Using 9.8 instead gives 784 N. The difference is a rounding convention, not a different law.

Example 4: elevator interpretation

For an 80 kg person accelerating upward at 2 m/s², the net upward force is $ma=160$ N. The scale reading is not 160 N; it is the normal force $N$ satisfying $N-mg=ma$ , so $N=m(g+a)$ .

Change acceleration sign while keeping mass positive. The force changes sign because the chosen direction has reversed.

math

F=(10)(3)=30\,N.

math

a=\frac{4500}{1500}=3\,m/s^2.

math

W=(80)(9.80665)=784.532\,N.

Principle and derivation

In modern notation, Newton's second law is more generally written as

F_{net}=\frac{dp}{dt}.

For constant mass, $p=mv$ , so $dp/dt=m\,dv/dt=ma$ . That is the familiar $F=ma$ form used by this calculator.

Dimensional analysis checks the unit immediately:

[kg]\,[m/s^2]=kg\cdot m/s^2=N.

Assumptions

The calculator uses the constant-mass form $F=ma$ .
Inputs represent one-dimensional signed values or magnitudes with a consistent direction convention.
The force entered is net force unless you explicitly build a free-body equation outside the calculator.
SI units are assumed by the fields.

Limitations

Supported:: solve any one of $F$ , $m$ , and $a$ from the other two, including signed values for opposite directions.
Approximate only:: real vehicles and elevators rarely maintain constant acceleration; the result is an average net force. Different choices of $g$ differ by about 0.1%.
Not covered:: free-body decomposition, friction and normal force models, multidimensional vectors, variable-mass systems, relativity, or rotational dynamics such as $\tau=I\alpha$ .
No unit conversion:: convert g to kg, km/h to m/s, or kgf/lbf to N before using the calculator.
Numerics:: inverse calculations with a zero denominator can produce infinity; extreme values may use scientific notation.

Common pitfalls

Entering weight in newtons into the mass field.
Treating one applied force as net force without accounting for friction, gravity, tension or normal force.
Mixing grams with kilograms.
Confusing zero velocity with zero acceleration; an object can be instantaneously at rest and still accelerate.

Typical use cases

Teaching

Connect a 1 kg mass to a weight of about 9.8 N, compare conventions for $g$ , distinguish net force from individual forces, and check dimensions.

Transport and machinery

Estimate drive or braking force for vehicle acceleration, dynamic loads in elevators and cranes, or friction demand when a conveyor starts.

Aerospace and sport

Relate thrust to launch acceleration, interpret “g” loads, or estimate the force involved in sprint starts and similar motions.

Everyday estimates

Estimate pushing or pulling force, or infer elevator acceleration from an apparent-weight change.

FAQ

Is mass the same as weight?

No. Mass is measured in kilograms and is an intrinsic property. Weight is the gravitational force $mg$ and is measured in newtons.

Why do textbooks use 9.8, 9.81 or 9.80665 for g?

9.80665 m/s² is the defined standard gravity. 9.81 and 9.8 are convenient rounded values; actual local gravity also varies slightly with latitude and altitude.

What does a negative force mean?

It means the net force points opposite the positive axis you chose. The physics is unchanged if you reverse the coordinate convention consistently.

Why can mass not be negative when acceleration can?

Mass is a scalar and always positive; acceleration is a vector, and its sign tells you the direction relative to the chosen positive axis. The panel rejects negative mass (the field has a min: 0 rule), and only the raw compute() does not forbid it; a negative-mass result has no physical meaning.

Privacy

All calculations happen locally in your browser. This page does not store your inputs.

Sources & review

Reviewed by: CalcX 编辑组
Updated: 2026-09-09

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