Newton’s Third Law Calculator

Related Calculators

Action force: The force of Object A on Object B. In this calculator, it is shown as Action force (Object A on Object B).

Reaction force: The force of Object B on Object A. It has the same size as the action force and the opposite direction [1][2].

Force magnitude: The size of a force without the sign. It tells you how strong the interaction is.

Positive direction: The direction you choose to count as positive, such as right or up. A negative result points the opposite way.

Mass: The amount of matter in an object, measured here in kilograms. Mass must be greater than 0.

Acceleration: How quickly velocity changes, measured in meters per second squared. A negative acceleration means the change is opposite your chosen positive direction.

Newton's 3rd law pair: Two interaction forces that are equal in size, opposite in direction, and act on different objects [1][3].

Mistake: Entering the same sign for Action force: force of Object A on Object B (N) and Reaction force: force of Object B on Object A (N) for the same interaction.
Fix: For one force pair, the two values must be equal in size and opposite in sign. If one is +50, the other must be -50 in the same sign convention.

Mistake: Using Mass (kg) as 0 or a negative number in Acceleration from force and mass (a = F/m) .
Fix: Enter a mass greater than 0. If you have grams, convert first so the value in Mass (kg) is correct.

Mistake: Entering 0 for Acceleration (m/s^2) in Mass from force and acceleration (m = F/a) .
Fix: This mode divides by acceleration, so Acceleration (m/s^2) cannot be 0. Use a nonzero acceleration or switch to a different mode.

Mistake: Mixing up which object goes with Mass of Object A, m1 (kg) and Mass of Object B, m2 (kg) in a two-object mode.
Fix: Keep the labels consistent all the way through. If Acceleration of Object A, a1 (m/s^2) belongs to Object A, its mass must be entered as Mass of Object A, m1 (kg) .

Mistake: Treating weight and normal force as a Newton's 3rd law pair when reading Force-pair note (if enabled) or Warnings (if any) .
Fix: A 3rd-law pair acts on different objects. Weight and normal usually act on the same object, so they are not a 3rd-law pair.

Mistake: Choosing Force unit for input and output as lbf, kN, or dyn but typing a value as if it were in newtons.
Fix: Match the number to the selected unit. If you enter 10 with lbf selected, the calculator reads it as 10 lbf, not 10 N.

• This calculator uses a one-dimensional sign model. It works best when you can describe the interaction as positive or negative along one line.
• In Interaction force from mass and acceleration (F = m*a), Acceleration from force and mass (a = F/m), and Mass from force and acceleration (m = F/a), the force is treated as the net force on one object along the chosen direction.
• The two-object relation m1*a1 = -(m2*a2) assumes the interaction force is the only unbalanced force causing motion in that direction. If other forces matter, real accelerations can differ.
• Mass inputs must be greater than 0, and Acceleration (m/s^2) cannot be 0 in mass-solving mode because that would divide by zero.
• Unit conversions are applied only to force units. Mass stays in kg, and acceleration stays in m/s^2.
• The misconception warning uses Context hint (optional) only as a teaching note. It does not change the math.
• Rounding and display format can make very small values look like 0 even when the stored result is not exactly zero.

Core idea

Newton's 3rd law says interaction forces come in pairs: same size, opposite direction, and on different objects [1][2]. That is why this calculator always treats Object A on Object B and Object B on Object A as a pair, not as two forces on the same object.

F_reaction = -F_action

Force, acceleration, and mass modes

When you use the single-object modes, the calculator applies Newton's 2nd law in one dimension. It reads the signed force, mass, and acceleration using your chosen positive direction.

F = m * a

a = F / m

m = F / a

If a mass result would be 0 or negative, the calculator blocks it as an error because physical mass must be greater than 0. That usually means the force sign and acceleration sign do not match the same object setup.

Two-object interaction modes

For the two-object modes, the calculator combines equal-and-opposite interaction forces with Newton's 2nd law for each object. In the ideal 1D case, this gives:

m1 * a1 = -(m2 * a2)

a2 = -(m1 * a1) / m2

a1 = -(m2 * a2) / m1

This is why the solved acceleration usually has the opposite sign from the known acceleration when both masses are positive.

Unit handling

Force inputs are converted to internal newtons first, then converted back to your selected output unit. Mass stays in kilograms, and acceleration stays in meters per second squared.

F_N = F_in * conv_to_N(unit)

1 lbf = 4.4482216152605 N

1 kN = 1000 N

1 dyn = 1e-5 N

Mini example

Suppose the mode is reaction from action force, and Action force: force of Object A on Object B (N) is +50 N. The calculator returns reaction force = -50 N and force magnitude = 50 N.

For a two-object example, let Mass of Object A, m1 (kg) = 90, Acceleration of Object A, a1 (m/s^2) = 20, and Mass of Object B, m2 (kg) = 30.

a2 = -(90 * 20) / 30 = -60 m/s^2

So Object B accelerates opposite the positive direction with magnitude 60 m/s^2.

Assumptions used in the calculation

The calculator ignores hidden inputs for the selected mode, blocks divide-by-zero cases, removes negative zero in display, and formats numbers in standard or scientific notation depending on your display choice. The force-pair explainer and misconception check are teaching notes only; they do not change the numeric physics result [2][3].