The Acceleration Calculator finds acceleration from initial velocity, final velocity, and time using Newton's kinematic equations. Supports all standard units and returns results in m/s², ft/s², and g-force — essential for physics students, engineers, and anyone analyzing motion.
4
m/s²
0.4077
g
50
m
10
m/s
4
m/s²
0.4077
g
50
m
10
m/s
The calculator for acceleration computes the rate of change of velocity using the fundamental kinematic equation of classical mechanics. Enter any two of the three variables — initial velocity, final velocity, and time — to find the third, along with the acceleration expressed in m/s², ft/s², and multiples of standard gravity (g).
Acceleration is the rate at which velocity changes with time. For uniform (constant) acceleration, the relationship is:
a = (v − u) / t
where a is acceleration (m/s²), v is final velocity (m/s), u is initial velocity (m/s), and t is time (s). A positive result means the object is speeding up in the direction of motion; a negative result (deceleration) means it is slowing down. Newton's Second Law connects this to force: F = ma, meaning acceleration is proportional to applied force and inversely proportional to mass. The velocity calculator solves the complementary problem of finding final velocity from acceleration and time.
For uniform acceleration, five equations (SUVAT) relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t):
Each equation omits one of the five variables, making it possible to solve any uniform acceleration problem with just three known values. The displacement calculator and uniformly accelerated motion calculator solve the other SUVAT combinations. Use this online calculator for the acceleration-specific case.
Standard gravity (g = 9.80665 m/s²) provides an intuitive reference for expressing acceleration. Common g-force values in everyday and engineering contexts:
The free fall calculator applies constant gravitational acceleration specifically, and the kinematics calculators category covers the full suite of motion analysis tools.
The acceleration calculator uses the fundamental kinematic equation for constant acceleration:
$$a = \frac{v - v_0}{t}$$
where a is the acceleration (m/s²), v is the final velocity (m/s), v₀ is the initial velocity (m/s), and t is the elapsed time (s).
Distance traveled under constant acceleration is computed using:
$$s = v_0 t + \frac{1}{2} a t^2$$
Substituting the expression for a:
$$s = v_0 t + \frac{1}{2} \left(\frac{v - v_0}{t}\right) t^2 = \frac{(v_0 + v)}{2} \cdot t$$
Average velocity for constant acceleration:
$$\bar{v} = \frac{v_0 + v}{2}$$
G-force conversion:
$$a_g = \frac{a}{9.81}$$
The results display the constant acceleration in m/s² and in g-forces, along with the total distance covered and average velocity during the interval. A positive acceleration means the object is speeding up in the positive direction, while a negative value means it is decelerating. For reference, Earth’s gravitational acceleration is 9.81 m/s² (1 g). Typical car acceleration is 2–4 m/s², while a cheetah can achieve about 10 m/s² during a sprint.
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Results
A sports car accelerates from rest to 100 km/h (27.78 m/s) in 4.5 seconds. The acceleration is 6.17 m/s² or about 0.63 g, and the car covers 62.5 meters during this time.
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A vehicle traveling at 30 m/s (108 km/h) brakes to a stop in 6 seconds. The deceleration is –5 m/s² (−0.51 g), and the braking distance is 90 meters.
Deceleration is simply acceleration in the direction opposite to the velocity, causing the object to slow down. In this calculator, deceleration appears as a negative acceleration value. Physically, there is no separate “deceleration force”—it is just acceleration with a negative sign relative to the direction of motion.
One g equals 9.81 m/s², which is the acceleration due to gravity at Earth’s surface. Expressing acceleration in g makes it easy to relate to human experience. Standing still you experience 1 g. A roller coaster might produce 3–4 g, and fighter pilots can experience up to 9 g. Sustained exposure to high g-forces can cause loss of consciousness.
Yes. Negative velocities simply indicate motion in the opposite direction to the chosen reference. For example, if you define forward as positive, then an object moving backward has a negative velocity. The calculator computes acceleration correctly regardless of the signs of the input velocities.
This calculator assumes constant (uniform) acceleration. If acceleration varies over time, the result will be the average acceleration over the interval. For variable acceleration, you would need calculus-based methods (integration of a(t)) or numerical simulation to get exact results.
The distance is computed using the kinematic equation s = v₀t + ½at². Under constant acceleration, this can also be written as s = (v₀ + v)/2 × t, which is the average velocity multiplied by time. Both expressions give the same result when acceleration is constant.
Walking: ~0.5 m/s². Family car: 2–4 m/s². Sports car: 5–8 m/s². Cheetah: ~10 m/s². Gravity (free fall): 9.81 m/s². Fighter jet: 30–90 m/s² (3–9 g). Space shuttle launch: ~30 m/s² (3 g).
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