Acceleration Calculator
Calculate acceleration from Newton's second law: enter the force applied in newtons and the object's mass in kilograms, and the calculator returns acceleration in m/s².
Calculate Acceleration From Force
Acceleration Formula
Where:
- \(a\) — acceleration \( (\mathrm{m/s^2}) \)
- \(F\) — net force acting on the object (N)
- \(m\) — mass of the object (kg)
This is Newton's second law of motion rearranged for acceleration. It states that an object's acceleration is directly proportional to the net force applied to it and inversely proportional to its mass.
Acceleration – Calculation Example
Example: a net force of 10 N is applied to a cart with a mass of 2 kg. Find its acceleration.
\[ a = \frac{F}{m} = \frac{10\ \mathrm{N}}{2\ \mathrm{kg}} = 5\ \mathrm{m/s^2} \]
Result: the cart accelerates at 5 m/s². These are the calculator's default values, so you can reproduce this result directly.
How to use the calculator
- Enter the net Force applied to the object in newtons (N). If several forces act, enter their sum — for example, 8 N forward minus 3 N backward gives 5 N.
- Enter the object's Mass in kilograms (kg).
- Read the Acceleration in meters per second squared (m/s²) in the result field.
The result is rounded to three decimal places. If you enter a mass of zero, the calculator returns ∞, because Newton's second law is undefined for a massless object.
What is acceleration?
Acceleration is the rate at which an object's velocity changes over time. An object accelerates whenever it speeds up, slows down, or changes direction. The SI unit is meters per second squared (m/s²): an acceleration of 5 m/s² means the velocity increases by 5 m/s every second the force is applied.
The calculator is based on Newton's second law of motion, one of the cornerstones of classical mechanics. In its general form the law reads \(F = ma\): the net force on an object equals its mass times its acceleration. Rearranging gives \(a = F/m\), the formula used here. It captures two intuitive facts: pushing harder makes an object speed up faster, and heavier objects accelerate less under the same force.
The value you obtain is instantaneous acceleration under a constant net force. If the force stays constant, the velocity grows linearly: after 1 s the cart in the example above moves at 5 m/s, after 2 s at 10 m/s, and so on. To explore the resulting motion, you can combine this result with our Projectile Motion Calculator or the Average Speed Calculator.
Interpreting the result
A positive result means the object accelerates in the direction of the net force; a negative net force produces a negative acceleration (deceleration) — for instance when friction or braking dominates. For comparison, everyday gravity produces about 9.81 m/s² at Earth's surface, which is the acceleration of any object in free fall. Race cars reach 10–15 m/s² under hard braking, and a passenger jet at takeoff accelerates at roughly 2–3 m/s². To express the result as a multiple of gravity, try the G-Force Calculator.
Assumptions and limitations
- Net force: the value you enter must be the sum of all forces acting on the object, not just one of them. Opposing forces such as friction or air resistance reduce the net force and therefore the acceleration.
- Constant mass: the formula assumes the mass does not change during the motion, which fails for rockets burning fuel or leaking containers.
- Classical mechanics: the result is valid at everyday speeds. Near the speed of light or for subatomic particles, relativistic effects make Newton's second law inaccurate.
- Constant force: the calculator gives instantaneous acceleration. If the force varies with time or position, the acceleration changes too and must be integrated to describe the full motion.
Quick reference values
| Force (N) | Mass (kg) | Acceleration (m/s²) |
|---|---|---|
| 10 | 2 | 5 |
| 50 | 10 | 5 |
| 100 | 20 | 5 |
| 20 | 4 | 5 |
| 98.1 | 10 | 9.81 |
Notice that doubling the force doubles the acceleration, while doubling the mass halves it — a direct illustration of the proportionalities in Newton's second law.
Frequently Asked Questions
How do I calculate acceleration by hand?
Divide the net force by the mass: \( a = F/m \). For example, a net force of 25 N on a 5 kg object gives \( 25/5 = 5\ \mathrm{m/s^2} \). Make sure the force is in newtons and the mass in kilograms before dividing — mixing units is the most common source of wrong answers.
How do I convert acceleration to g-forces or km/h per second?
To express acceleration in g, divide the result by 9.81 — for example, 19.62 m/s² is exactly 2 g. To convert to km/h per second, multiply by 3.6, since 1 m/s = 3.6 km/h. So 5 m/s² equals 18 km/h gained every second.
Why is my acceleration negative, and what does that mean?
A negative value means the net force points opposite to the chosen positive direction, so the object slows down (decelerates) or accelerates backward. This often happens when friction, braking, or drag exceeds the driving force. Just enter the net force with its sign: 8 N forward minus 12 N of friction gives −4 N and a negative result.
Can I use this calculator with pounds, slugs, or other non-SI units?
The calculator assumes newtons and kilograms. With other units you must convert first: 1 lbf ≈ 4.448 N and 1 lb ≈ 0.4536 kg. Note that pounds measure weight (a force), not mass — dividing pounds-force by pounds-mass actually works in the imperial system and yields acceleration in g-units, so multiply by 32.17 to get ft/s².
How do I find how fast the object is moving after some time?
If the force (and thus acceleration) stays constant, multiply acceleration by time: \( v = a \cdot t \). An object accelerating at 5 m/s² for 4 s reaches 20 m/s. The distance traveled from rest is \( s = \tfrac{1}{2} a t^2 \). These follow-up calculations turn the acceleration value into a full description of the motion.
What's the difference between mass and weight when entering values?
Mass is the amount of matter, measured in kilograms; weight is the gravitational force on that mass, measured in newtons. Only mass goes into the Mass field. If you know an object's weight (e.g., 98.1 N), convert it first: \( m = W/9.81 \), which gives 10 kg in this case. Entering weight as mass makes the result about 9.81 times too small.
What happens if the mass changes during motion, like a rocket?
Newton's second law with constant mass no longer applies. A rocket burning fuel loses mass continuously, so its acceleration increases over time even with constant thrust. The simple \( a = F/m \) result is only valid at one instant with the current mass. For rockets and similar systems you need the variable-mass (Tsiolkovsky) equations instead.