Inclined plane calculator

Type angle α [°]. The calculator computes a = g sin α: at 30° that is about 4.9 m/s². Length L [m] is optional: 5 m at 30° is about 1.43 s and 7 m/s. Here μ = 0.

Inputs

Result

Angle α (degrees), Ramp length L (optional) and g (default 9.81). The result shows up here.

How it works

a α a = g sin(α) L
With no friction, acceleration along the incline is the component of g: a = g·sin(α).

With no friction, acceleration along the board is a = g sin α. At 30°, sin 30° = 1/2, so a = 9.81 × 0.5 ≈ 4.91 m/s², about 4.9 on the page. From rest over L = 5 m: t = √(2L/a) ≈ 1.43 s, vₖ = √(2 a L) ≈ 7.0 m/s. At 45° and 4 m, a ≈ 6.94 m/s², t ≈ 1.07 s, vₖ ≈ 7.45 m/s. At 10° and 20 m, a ≈ 1.70 m/s², t ≈ 4.85 s, vₖ ≈ 8.25 m/s.

At 25° and 8 m, a ≈ 4.15 m/s², t ≈ 1.96 s. At 15° and 6 m, a ≈ 2.54 m/s², t ≈ 2.17 s. At 80° and 3 m, a is close to g, about 9.66 m/s². At 30°, 5 m and g = 1.62 m/s² (classroom Moon) a = 0.81 m/s², t ≈ 3.51 s, vₖ ≈ 2.85 m/s. Mass does not enter: with no friction a = g sin α.

The first field is α in degrees, not radians. L is optional, in meters. Empty g fills 9.81. Blank L means you want a alone, not t and vₖ. Typed 0° gives a = 0: the board lies flat. α needs a number before 4.9 m/s² can appear. A comma and a period are the same angle: 30,5 and 30.5.

The model has μ = 0. Air drag does not sit here. With kinetic friction, open the incline with μ: at 30° and 0.2, a drops to about 3.21 m/s². T = μ N alone is on friction force.

t and vₖ assume a start from rest. If the block is already moving, use SUVAT or accelerated motion with a v₀. This calculator does not ask for v₀.

Type 30, add 5, click Calculate, and match a ≈ 4.9 m/s², t ≈ 1.43 s, vₖ ≈ 7 m/s. Then change g to 1.62 and watch a slower slide. The header symbol does not grease the board.

With friction: incline with μ. T alone: friction force.

How to use

  1. Type angle α in degrees, for example 30. The field wants degrees, not radians.
  2. Leave L blank for a alone, or type 5 m for time and vₖ from rest.
  3. Leave g blank for Earth (9.81). On the lunar example type 1.62.
  4. Click Calculate. 30° and 5 m give a ≈ 4.9 m/s², t ≈ 1.43 s, vₖ ≈ 7 m/s.
  5. With friction, open the incline with μ. T alone is on friction force.

Formula

a = g sin(α)

From rest over length L:

t = √(2L/a), vk = √(2a L)

No friction (μ = 0).

a, α, and L on a smooth ramp

Frictionless inclined plane: a = g sin α. At 30° that is about 4.9 m/s². L = 5 m also gives t ≈ 1.43 s and vₖ ≈ 7 m/s. μ = 0.

a
Acceleration [m/s²]. 9.81 × sin 30° ≈ 4.91. Half of g at 30°.
α
Ramp angle [°]. 30 or 10. Not radians.
L
Optional length [m]. 5 m or 20 m. Without L you keep a only.
g
Optional 9.81 m/s². 1.62 on the Moon. A blank field takes Earth.

Real-life examples

Example 1

α = 30°, g = 9.81 m/s².

Example 2

α = 30°, L = 5 m.

Example 3

α = 10°, L = 20 m.

Example 4

α = 45°, L = 4 m.

Example 5

α = 25°, L = 8 m.

Example 6

α = 15°, L = 6 m.

Example 7

α = 30°, L = 5 m, g = 1.62 m/s².

Example 8

α = 80°, L = 3 m: a near g.

Ways to use this calculator

  • You check a on a 30° board with no friction.
  • You compute the 5 m slide time at 30°.

Related calculators

a from Δv and t
Free fall, no incline and no launch angle.
Force and acceleration on a slope
The same Newton-II physics, a different unknown.
Energy from starting height
Potential energy from height h = L sin α on the ramp.
The α → 90° limit
Straight free fall, no horizontal speed.
Uniformly Accelerated Motion
Distance and final speed at constant acceleration.

All physics calculators

Frequently asked questions

How much a at 30°?

Acceleration is about 4.91 m/s², order 4.9 on the page. That is 9.81 × 0.5, half of g. No friction.

How much t and vₖ over 5 m at 30°?

Time is about 1.43 s, final speed about 7.0 m/s. Start from rest, g = 9.81, L = 5 m.

Which units do I type?

Angle α [°], optional L [m] and g [m/s²]. Blank g is 9.81. Result a [m/s²], and with L also t [s] and vₖ [m/s].

Do I have to type L?

No. Without L you only get a. With L you also get t and vₖ, start from rest, no μ field.

How much at 10° and L = 20 m?

You get a about 1.70 m/s², t about 4.85 s and vₖ about 8.25 m/s. A gentler angle, a longer ramp.

Is the angle in radians?

No. The field wants degrees. Typed 30 is thirty degrees, not 30 rad.

Where is friction?

On the incline-with-friction page. Here μ = 0. At 30° and μ = 0.2, a drops to about 3.21 m/s².

Does mass enter a?

With no friction a = g sin α, mass cancels. A heavier block slides at the same a.

How much at 30°, 5 m and g = 1.62 m/s²?

On the Moon a = 0.81 m/s², t about 3.51 s, vₖ about 2.85 m/s. Same 30° and 5 m, another g.

Does a comma in 30.5 work?

Yes. 30.5 and 30,5 are the same α [°]. A comma and a period mean the same value.

Knowledge sources

The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.

Page updated in 2026.