Newton's Second Law Calculator
Enter mass and acceleration to compute the net force F = m·a instantly.
Input Data
Results
At a glance:Newton's second law of motion (Newton, 1687) states that an object's acceleration a is proportional to the net external force F and inversely proportional to its mass m, in the same direction as the force: F = m·a (or generally F = dp/dt, the rate of change of momentum, which reduces to F = m·a for constant mass). Forms: F = m·a, a = F/m, m = F/a. The unit newton is defined by 1 N = 1 kg·m/s². Crucially F is the net force (vector sum of all forces); if forces cancel, acceleration is zero (Newton's first law). Example: m = 10 kg, a = 2 m/s² → F = 20 N. Weight W = m·g is a special case of the second law under gravity.
Formula
Newton's second law: F = m·a
Rearranged: a = F/m, m = F/a
Units: 1 N = 1 kg·m/s²; weight W = m·g
$$F = m a$$$$a = \dfrac{F}{m}, \quad m = \dfrac{F}{a}$$How to Use
- Enter the mass m (kg).
- Enter the acceleration a (m/s²).
- The calculator returns the net force F = m·a (N).
Case Studies
Pushing a shopping cart
10 kg cart to accelerate at 2 m/s².
F = 10×2 = 20 N.
Add 10 kg load (20 kg total): same 20 N gives only a = 20/20 = 1 m/s².
Mass from weight
g ≈ 9.81, weight 98.1 N.
m = 98.1/9.81 = 10 kg.
Weight is the second law under gravity; use m = F/a to recover mass.
FAQ
Which force is F in F = m·a?
The net (resultant) force — the vector sum of all external forces, not a single one. If forces cancel, a = 0. Draw a free-body diagram first.
What is the difference between newton and kilogram?
Kilogram is mass (amount of matter, inertia); newton is force (and weight). Linked by 1 N = 1 kg·m/s². A 1 kg mass weighs ~9.81 N on Earth (W = m·g) but its mass is unchanged.
Are mass and weight the same?
No. Mass m is intrinsic; weight W = m·g depends on local gravity and changes with location (lighter on the Moon, same mass).
Does the second law always hold?
In inertial frames at everyday speeds (≪c) and macroscopic scales. Near light speed use special relativity; for microscopic particles use quantum mechanics; for varying mass (rockets) use F = dp/dt.
Is force direction always the same as acceleration?
Yes. Acceleration is always in the direction of the net force (m > 0). Note acceleration need not point along velocity — during deceleration the net force opposes motion (negative acceleration/braking).
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.