Magnitude of Acceleration Calculator

Magnitude of Acceleration Calculator finds the size of an acceleration from its components, a velocity change, force and mass, or circular motion. It also compares it with gravity.

Magnitude of Acceleration Calculator Inputs

The magnitude of acceleration is the size of the acceleration with its direction left out. It is a single positive number in meters per second squared. The Magnitude of Acceleration Calculator reaches it from six different starting points, picked under Calculate From.

Vector Components takes the x, y and z parts of the acceleration. Two Velocity Vectors takes a velocity before and after with the time between them. Force and Mass uses Newton’s second law, and Velocity and Time handles straight-line motion.

Distance and Time works from how far something travelled under steady acceleration. Circular Motion gives the centripetal acceleration from a speed and a radius. Every setting returns the same kind of answer, so results from different problems can be compared.

The cards put the number in context. They show it in g, in ft/s² and in km/h per second, the time it would take to go from 0 to 100 km/h, and the net force on a chosen mass. A table then places it beside the surface gravity of the Moon, Mars, Earth and Jupiter.

Magnitude of Acceleration Formula

There is no single formula for magnitude of acceleration. The right one depends on what is known. When the acceleration is given by its components, the magnitude is the length of the vector, found with the Pythagorean theorem in three dimensions.

$$|a| = \sqrt{a_x^2 + a_y^2 + a_z^2}$$

The Vector Components setting of the Magnitude of Acceleration Calculator applies this line. Components of 3 and 4 m/s² give 5 m/s², and components of 2, 3 and 6 m/s² give 7 m/s². This is also how to calculate total magnitude when an object accelerates along two or three axes at once.

The magnitude of average acceleration formula uses the change in velocity over a time interval. With velocity vectors, subtract them first and then take the size of the difference. In one dimension this is simply the final velocity minus the initial velocity, with the sign dropped.

$$|a| = \frac{|v_1 – v_0|}{\Delta t}$$

A magnitude of acceleration calculator with mass needs the net force as well. Newton’s second law says acceleration equals net force divided by mass. A net force of 300 N on 60 kg gives 5 m/s².

$$|a| = \frac{|F|}{m}$$

The acceleration formula with distance and time assumes the acceleration is steady. From rest, the distance covered is half the acceleration times the time squared. Solving for the acceleration, with a starting speed v₀ allowed, gives the line below.

$$a = \frac{2 (d – v_0 t)}{t^2}$$

The magnitude of acceleration formula for circular motion is the speed squared over the radius. The speed can stay constant, because the direction of the velocity keeps turning. This acceleration points at the center of the circle.

$$a = \frac{v^2}{r}$$

Magnitude of Acceleration Examples

The table runs one example through each setting of the Magnitude of Acceleration Calculator. The first five rows are the values each setting opens with, and the last is a textbook case.

The jet row comes from OpenStax University Physics, which asks what radius gives a pilot 1 g in a level turn at 134.1 m/s. Its answer is 1,835 m, and entering that radius returns 9.8 m/s².

The second row shows why vectors must be subtracted before taking a size. The velocity change is (4, 8) m/s, which has a size of 8.94 m/s. Dividing by 4 s gives 2.24 m/s², pointing 63.43° from the x-axis.

A velocity can also turn without changing speed. Going from 10 m/s east to 10 m/s north in 5 s is a velocity change of 14.14 m/s, so the magnitude is 2.83 m/s². The Magnitude of Acceleration Calculator flags this case as steady speed with a changing direction.

Magnitude Given Velocity and Time

To find the magnitude of acceleration given velocity and time, subtract the initial velocity from the final one and divide by the time. Going from 10 to 25 m/s in 6 s is a change of 15 m/s, so the magnitude is 2.5 m/s². The object covers 105 m while it happens.

Slowing down gives the same kind of answer. A car braking from 25 m/s to rest in 4 s has an acceleration of −6.25 m/s², and its magnitude is 6.25 m/s², or 0.64 g. Negative acceleration of this kind is called deceleration, or retardation in some textbooks.

This is the difference between acceleration and the magnitude of acceleration. Acceleration is a vector with a direction, and in one dimension the direction shows up as a sign. The magnitude keeps only the size, so it is never negative.

On a velocity-time graph, the magnitude is the steepness of the line. To find the greatest magnitude of acceleration over a trip, look for the steepest section, whether it slopes up or down. For constant acceleration, the Displacement Calculator turns the same values into distance.

How Large Is the Result?

The comparison table in the Magnitude of Acceleration Calculator uses surface gravity as a yardstick, with values from the NASA Planetary Fact Sheet. Standard gravity on Earth is 9.80665 m/s², which defines 1 g.

The third card reverses the car example. An acceleration of 5 m/s² would take something from rest to 100 km/h in 5.56 s over 77.16 m. The fourth card gives the force behind it, which is 350 N on a 70 kg person.

The same card shows apparent weight. A 70 kg person weighs 686.47 N at rest and would read 1,036.5 N on a scale while accelerating upward at 5 m/s². An object in free fall has an acceleration of exactly 1 g, the case covered by the Free Fall Calculator.

Units and Meaning of Magnitude

What is the SI unit of acceleration?

The SI unit of acceleration is the meter per second squared, m/s². It is a derived unit, built from the meter for distance and the second for time. Magnitude is measured in the same unit as the quantity itself, so the magnitude of an acceleration is also in m/s². The Magnitude of Acceleration Calculator accepts ft/s² and g as well and converts them.

SI stands for Système International d’Unités, the International System of Units. It has seven base units, which are the second, meter, kilogram, ampere, kelvin, mole and candela. Every other unit, including m/s² and the newton, is derived from these.

What is meant by magnitude?

Magnitude means size without direction. For a plain number it is the absolute value, so the magnitude of 2 is 2 and the magnitude of −10 is 10. For a vector it is the length of the arrow, found from its components.

Magnitude does not mean speed, but the two are linked. Speed is the magnitude of velocity, in the same way that the result here is the magnitude of acceleration. A force of 300 N to the left has a magnitude of 300 N.

What are the four types of acceleration?

Textbooks usually list uniform, non-uniform, average and instantaneous acceleration. Uniform acceleration stays constant, as in free fall without air. Non-uniform acceleration changes with time, average acceleration covers a whole interval, and instantaneous acceleration is the value at one moment.

In the Magnitude of Acceleration Calculator, the Velocity and Time setting returns an average over the interval. The Distance and Time setting assumes uniform acceleration. Problems where a force sets the motion on a slope are handled by the Inclined Plane Calculator.

What are the three formulas for acceleration?

The three most used are a = Δv ÷ Δt from a velocity change, a = F ÷ m from force and mass, and a = 2(d − v₀t) ÷ t² from distance and time. The Magnitude of Acceleration Calculator covers all three and adds the component and circular forms.

In math classes the same idea appears as the second derivative of position with respect to time. For steady acceleration the derivative reduces to the first formula, the change in velocity divided by the time taken.