Acceleration Converter

Acceleration Converter Guide: m/s², ft/s², g, Gal, cm/s², and More

Acceleration measures how quickly velocity changes with time. Because velocity itself measures change in position per unit time, acceleration contains time squared in its denominator.

The SI derived unit of acceleration is the metre per second squared, written m/s². BIPM lists acceleration among SI derived quantities with unit m/s².

An acceleration of 1 m/s² means velocity changes by 1 meter per second during each second when the acceleration is constant and aligned with the velocity axis being considered.

This is different from velocity. A vehicle moving steadily at 30 m/s can have zero acceleration if neither the magnitude nor direction of its velocity changes. Conversely, an object can accelerate even while its speed remains constant if its direction changes.

Acceleration units combine a length unit with a squared time denominator. Converting from feet per second squared to meters per second squared therefore changes the length unit but does not square the length conversion factor, because acceleration contains only one power of length.

NIST gives 1 foot per second squared as exactly 0.3048 meter per second squared because one international foot is exactly 0.3048 meter.

Likewise, 1 inch per second squared equals exactly 0.0254 m/s² because one international inch equals exactly 0.0254 meter.

The Gal, named after Galileo, is a centimeter-per-second-squared unit commonly encountered in gravimetry and geophysics. NIST gives 1 Gal = 0.01 m/s².

Another common acceleration reference is standard gravity, written gₙ or often simply g in ordinary engineering usage. Standard gravity is defined as exactly 9.80665 m/s².

Standard gravity is a conventional reference value. It is not a claim that local gravitational acceleration everywhere on Earth equals exactly 9.80665 m/s². Actual local gravitational acceleration varies with latitude, elevation, and other geophysical factors.

A statement such as “2 g” therefore means acceleration equal to twice standard gravity, or 19.6133 m/s². It does not mean the object has doubled its mass or that gravitational acceleration at its location is literally two times Earth gravity.

This calculator converts acceleration units only. It does not determine acceleration from velocity and time or solve motion equations. Those belong to a kinematics or acceleration-solving calculator rather than a unit converter.

How to Convert Acceleration Units Correctly

Enter the acceleration value: Positive, negative, fractional, decimal, or scientific-notation values can be converted.
Choose the source unit: Select m/s², cm/s², km/s², ft/s², in/s², Gal, standard gravity g, or another supported acceleration unit.
Choose the target unit: Select the acceleration unit into which the value should be converted.
Preserve the sign: Negative acceleration remains negative after unit conversion because conversion changes units rather than direction.
Use standard gravity for g-force: When converting g values, use the conventional standard gravity value of 9.80665 m/s².
Review the conversion factor: Display the source and target relationships with m/s² so the result can be independently checked.
Round only the displayed result: Carry the full defined conversion precision internally before formatting the output.

Formula and variables

A robust converter expresses every supported acceleration unit relative to one canonical unit, preferably m/s². Convert the source value to m/s² using its factor, then divide by the target unit’s m/s² factor. This produces consistent reciprocal conversions without maintaining a separate factor for every possible unit pair.

Converted Acceleration = Original Acceleration × Source-to-SI Factor ÷ Target-to-SI Factor

a₁ — Original acceleration: The numerical acceleration in the source unit.
a₂ — Converted acceleration: The same acceleration expressed in the target unit.
F₁ — Source SI factor: The number of m/s² represented by one source unit.
F₂ — Target SI factor: The number of m/s² represented by one target unit.

Scenario 1: Convert 2 g to Meters per Second Squared

An acceleration is reported as 2 times standard gravity and needs to be expressed in SI units.

Acceleration: 2 g
Standard gravity: 9.80665 m/s² per g

Use 1 g = 9.80665 m/s².
Multiply 2 × 9.80665.
2 × 9.80665 = 19.6133.

Result: 2 g = 19.6133 m/s².

The result represents acceleration equal to twice the conventional standard-gravity reference.

Understanding your results

Converted acceleration

This represents exactly the same acceleration magnitude in another unit.

Only the numerical value and unit representation change.

Standard gravity

The g unit is based on the conventional standard-gravity value 9.80665 m/s².

It should not be confused with a precise measurement of local gravitational acceleration.

Signed acceleration

A negative sign commonly indicates acceleration opposite the selected positive coordinate direction.

The conversion preserves that sign.

Gal

The Gal is a centimeter-per-second-squared acceleration unit.

One Gal equals 0.01 m/s².

Assumptions

All supported units represent linear acceleration rather than angular acceleration.
The canonical internal acceleration unit is m/s².
International foot and inch definitions are used.
One international foot equals exactly 0.3048 meter.
One international inch equals exactly 0.0254 meter.
One Gal equals 0.01 m/s².
Standard gravity gₙ equals exactly 9.80665 m/s².
The conversion preserves the sign of the entered acceleration.
No kinematic calculation is performed because the acceleration value is already known.

Limitations

Acceleration conversion does not calculate acceleration from distance, velocity, or time.
Linear acceleration and angular acceleration are different physical quantities and should not share the same converter without explicit dimensional handling.
Standard gravity is a defined reference acceleration, not the exact local gravitational field everywhere on Earth.
Actual free-fall acceleration varies geographically and with altitude.
A g-force value can describe proper acceleration experienced by an object or person in contexts where coordinate acceleration requires more nuanced interpretation.
Velocity units such as m/s, mph, and km/h are not acceleration units.
Expressions such as mph/s can represent acceleration but require conversion of both the velocity unit and the time interval consistently.
Force and acceleration are related by Newton’s second law but are not interchangeable quantities.
Very large or very small values can require scientific notation to avoid unreadable decimal strings.
Rounding the standard-gravity value to 9.8 or 9.81 changes the result slightly compared with using the conventional exact reference 9.80665.

Common mistakes

Confusing acceleration with velocity.
Treating m/s² as though it were m²/s.
Squaring the foot-to-meter conversion factor when converting ft/s² to m/s².
Assuming one g equals exactly 10 m/s².
Assuming standard gravity is the exact local gravity everywhere.
Converting Gal as though it were 1 m/s².
Dropping a negative acceleration sign during conversion.
Converting angular acceleration in rad/s² with a linear-acceleration converter.
Treating acceleration expressed in mph/s as though mph itself were an acceleration unit.
Rounding conversion factors before completing the calculation.

Practical use cases

Scenario 2: m/s² to ft/s²

Convert 5 m/s².

Since 1 ft/s² = 0.3048 m/s², divide 5 by 0.3048 to obtain approximately 16.4042 ft/s².

Scenario 3: ft/s² to m/s²

Convert 32.174 ft/s².

Multiply by 0.3048 to obtain approximately 9.80664 m/s².

Scenario 4: m/s² to g

Convert 19.6133 m/s².

Divide by 9.80665 to obtain exactly 2 g.

Scenario 5: Gal to m/s²

Convert 250 Gal.

250 × 0.01 = 2.5 m/s².

Scenario 6: cm/s² to Gal

One Gal equals one centimeter per second squared.

Therefore 75 cm/s² = 75 Gal.

Planning and decision guide

Acceleration describes change in velocity over time

For average acceleration, a = Δv/Δt.

The unit therefore has velocity divided by time, producing length/time².

Scenario 7: Velocity changes by 10 m/s in 2 seconds

Average acceleration = 10/2.

The result is 5 m/s².

Acceleration is a vector quantity

It has both magnitude and direction.

A unit converter changes only the unit representation, not the physical direction.

Negative acceleration is coordinate-dependent

A negative sign means acceleration points opposite the chosen positive axis.

It does not automatically mean the object is slowing down.

Scenario 8: Moving left and accelerating left

If right is positive, both velocity and acceleration can be negative.

The object can speed up even though acceleration is numerically negative.

Deceleration is not a separate physical unit

Deceleration ordinarily means acceleration opposite the direction of motion.

It is still measured in the same units such as m/s².

The SI unit is metre per second squared

BIPM lists acceleration with SI derived unit m/s².

The dimension is length multiplied by time to the power −2.

m/s² should not be read as square meters per second

The exponent applies to seconds in the denominator.

It means meters per second per second.

Scenario 9: 3 m/s² for 4 seconds

With constant acceleration along one axis, velocity changes by 3 m/s each second.

After four seconds, the velocity change is 12 m/s.

Centimeter per second squared follows ordinary metric scaling

One centimeter equals 0.01 meter.

Therefore 1 cm/s² = 0.01 m/s².

Scenario 10: 500 cm/s²

500 × 0.01 = 5.

Result = 5 m/s².

Kilometer per second squared is much larger

One kilometer equals 1,000 meters.

Therefore 1 km/s² = 1,000 m/s².

Time is not converted when seconds remain seconds

Converting cm/s² to m/s² changes only the numerator length unit.

The denominator remains seconds squared.

Foot per second squared converts linearly with foot

NIST gives 1 ft/s² = 0.3048 m/s².

The factor is 0.3048 rather than 0.3048² because only the numerator contains a length dimension.

Scenario 11: 10 ft/s²

10 × 0.3048 = 3.048.

Result = 3.048 m/s².

Inch per second squared uses the exact inch definition

NIST gives 1 in/s² = 0.0254 m/s².

Because 12 inches equal one foot, 12 in/s² equals 1 ft/s².

Scenario 12: 120 in/s²

120 × 0.0254 = 3.048.

The result is also 10 ft/s².

The Gal is exactly 1 cm/s²

NIST gives one Gal as 0.01 m/s².

Therefore Gal and cm/s² have identical numerical values.

Gal is commonly used in gravimetry

Earth gravitational-field variations are often much smaller than one Gal.

Subunits such as milligal can therefore be useful in geophysical work.

Milligal is one-thousandth of a Gal

1 mGal = 0.001 Gal.

Therefore 1 mGal = 10⁻5 m/s².

Scenario 13: 50 mGal

50 × 10⁻5 m/s² = 5 × 10⁻4 m/s².

The acceleration is 0.0005 m/s².

Standard gravity is a defined conventional value

NIST gives standard acceleration of free fall gₙ = 9.80665 m/s².

It is used as a reference in engineering, metrology, and acceleration comparisons.

Scenario 14: Half a g

0.5 × 9.80665.

Result = 4.903325 m/s².

One g in ft/s² uses the international foot

Divide 9.80665 m/s² by 0.3048 m per ft.

The result is approximately 32.17404856 ft/s².

Scenario 15: 3 g in ft/s²

1 g ≈ 32.17404856 ft/s².

3 g ≈ 96.52214567 ft/s².

g-force is dimensionless when expressed as a ratio

A value such as 2 g means acceleration divided by standard gravity equals 2.

The word “g” is commonly used as a convenient acceleration unit even though the ratio itself is dimensionless.

g-force does not mean grams

The lowercase g can also denote gram in mass contexts.

The interface should label acceleration clearly as “standard gravity (g)” to avoid ambiguity.

Scenario 16: 5 g acceleration

This means five times standard gravitational acceleration.

It does not mean five grams of mass.

Standard gravity and local gravity are different concepts

Standard gravity is defined exactly.

Actual terrestrial gravitational acceleration varies with latitude, altitude, and local geology.

Scenario 17: Local gravity measurement

A gravimeter may measure a local value slightly different from 9.80665 m/s².

That does not change the definition of 1 standard g.

Free-fall acceleration is commonly approximated in textbook problems

Introductory problems often use 9.8 m/s² or 9.81 m/s² for convenience.

Those are approximations, while standard gravity is defined as 9.80665 m/s².

Do not silently replace standard gravity with 9.8

Conversion involving the unit g should use the defined conventional value.

Simplified physics problems can use 9.8 only when the problem explicitly specifies that approximation.

Miles per hour per second is also acceleration

mph/s means velocity changes by a certain number of miles per hour during each second.

It can be converted by first converting the mph velocity increment into m/s.

Scenario 18: 1 mph/s

1 mph ≈ 0.44704 m/s.

Therefore 1 mph/s = 0.44704 m/s².

Kilometers per hour per second can also be converted

1 km/h = 1/3.6 m/s.

Therefore 1 (km/h)/s ≈ 0.277777778 m/s².

Hours squared are different from per-second velocity change

km/h² and (km/h)/s are different units.

The time denominators must be interpreted explicitly before conversion.

Scenario 19: Why km/h² is not km/h/s

km/h² describes velocity change per hour, with hour appearing twice in the dimension.

(km/h)/s uses one hour inside the velocity unit and one second for the rate of change.

Unit parsing should preserve parentheses

Write (km/h)/s when necessary to distinguish it from km/h².

Ambiguous textual labels can produce large conversion errors.

Acceleration and force are related by F = ma

Newton’s second law connects net force, mass, and acceleration.

Acceleration itself remains a distinct quantity with unit m/s².

Scenario 20: Same acceleration, different masses

Two objects can both accelerate at 5 m/s².

The more massive object requires a larger net force to produce that acceleration.

Do not convert newtons into m/s² without mass

A force cannot be turned into acceleration through a simple unit conversion alone.

The mass and physical relationship F = ma are required.

Acceleration can occur without a speed change

Velocity includes direction as well as magnitude.

Uniform circular motion has centripetal acceleration even when speed is constant.

The Angle Conversion Calculator handles angular units

Angular acceleration is measured in units such as rad/s².

It should remain separate from linear acceleration in m/s².

Angular and linear acceleration can be related physically

Tangential acceleration can be written a_t = rα when α is angular acceleration in radians per second squared.

That relationship requires radius and is a calculation, not a direct unit conversion.

Sign should always survive conversion

−5 m/s² converts to approximately −16.4042 ft/s².

Changing units cannot reverse the vector direction represented by the sign.

Scenario 21: Negative acceleration

Input = −9.80665 m/s².

Equivalent = −1 g.

Scientific notation helps with gravimetry values

Very small accelerations can be more readable as powers of ten.

For example, 1 μGal corresponds to 10⁻8 m/s².

Microgal is useful for extremely small acceleration variations

1 μGal = 10⁻6 Gal.

Since 1 Gal = 10⁻2 m/s², 1 μGal = 10⁻8 m/s².

Scenario 22: 250 μGal

250 × 10⁻8 m/s².

Result = 2.5 × 10⁻6 m/s².

The converter should use one canonical base unit

Store every unit as a factor relative to m/s².

Conversion then becomes source → m/s² → target.

Recommended internal architecture

converted = value × sourceFactor / targetFactor.

This avoids maintaining independently rounded conversion pairs.

Scenario 23: ft/s² to g through SI

Convert ft/s² to m/s² using 0.3048.

Then divide by 9.80665 m/s² per g.

Canonical conversion improves round-trip accuracy

Converting a value from unit A to unit B and back should reproduce the original value within floating-point display tolerance.

Large round-trip differences can indicate a bad conversion factor.

The strongest result shows several common equivalents

Even when one target is selected, an expandable panel can show m/s², ft/s², g, and Gal together.

This makes the scale of the acceleration easier to understand.

Frequently asked questions

What is acceleration?

Acceleration is the rate at which velocity changes with time.

What is the SI unit of acceleration?

Metre per second squared, m/s². BIPM lists m/s² as the SI derived unit of acceleration.

What does m/s² mean?

It means meters per second per second: the velocity changes by that many meters per second during each second under constant acceleration.

Is acceleration the same as speed?

No. Speed measures how fast something moves; acceleration measures how velocity changes.

Can acceleration be negative?

Yes. The sign indicates direction relative to the selected coordinate axis.

Does negative acceleration always mean slowing down?

No. If velocity is also negative, negative acceleration can increase speed.

How do I convert ft/s² to m/s²?

Multiply by 0.3048. NIST gives 1 ft/s² = 0.3048 m/s².

How do I convert m/s² to ft/s²?

Divide by 0.3048, or multiply by approximately 3.280839895.

How do I convert in/s² to m/s²?

Multiply by 0.0254.

What is one g in m/s²?

Standard gravity is exactly 9.80665 m/s².

What is one g in ft/s²?

Approximately 32.17404856 ft/s² using the international foot.

How do I convert m/s² to g?

Divide the acceleration by 9.80665.

How do I convert g to m/s²?

Multiply the number of g by 9.80665.

Is g exactly 9.8 m/s²?

No. Standard gravity is defined as exactly 9.80665 m/s². Values such as 9.8 or 9.81 are common approximations.

Is standard gravity the same as gravity everywhere on Earth?

No. It is a conventional reference value. Actual local gravitational acceleration varies.

What is a Gal?

A Gal is a unit of acceleration equal to 1 centimeter per second squared, or 0.01 m/s².

How many Gal are in 1 m/s²?

100 Gal.

Is cm/s² the same as Gal?

Numerically yes: 1 cm/s² = 1 Gal.

What is a milligal?

One milligal is 0.001 Gal or 10⁻5 m/s².

What is a microgal?

One microgal is 10⁻6 Gal or 10⁻8 m/s².

How do I convert cm/s² to m/s²?

Multiply by 0.01.

How do I convert km/s² to m/s²?

Multiply by 1,000.

What is 1 mph per second in m/s²?

Approximately 0.44704 m/s².

Is mph an acceleration unit?

No. mph is a velocity unit. mph per second can describe acceleration.

Is rad/s² an acceleration unit?

It is an angular-acceleration unit, not a linear-acceleration unit.

Can I convert rad/s² directly to m/s²?

Not through unit conversion alone. A physical relationship such as tangential acceleration a = rα requires the radius.

Can I convert force directly to acceleration?

No. Force and acceleration are related by F = ma, so mass is required.

Why is ft/s² converted with 0.3048 instead of 0.3048²?

Acceleration contains one length dimension divided by time squared. Only the length unit changes from feet to meters.

Can an object accelerate at constant speed?

Yes. Changing direction changes velocity, so uniform circular motion has acceleration even at constant speed.

What is Earth gravity approximately?

Introductory physics often uses approximately 9.8 or 9.81 m/s², while standard gravity is defined as exactly 9.80665 m/s².

How accurate is an acceleration converter?

For defined unit relationships such as the international foot and standard gravity, conversion can be exact before display rounding. The precision of the original measured acceleration is a separate issue.

Sources and review

NIST Guide to the SI, Appendix B.9 — Acceleration Conversion Factors — National Institute of Standards and Technology. Accessed 2026-09-01.
NIST Guide to the SI, Appendix B.8 — Unit Conversion Factors — National Institute of Standards and Technology. Accessed 2026-09-01.
Resolution 12 of the 11th CGPM — SI Derived Units — Bureau International des Poids et Mesures. Accessed 2026-09-01.

Reviewed 2026-09-01 by Dr Akawak Ejigu, DBA.