Physics calculator

Incline Slip or Tip Calculator

Q: What does either mean?

θ_slip and θ_tip are the same, so both modes are impending at that angle.

Q: Is this a horizontal force on a level surface?

That case is the slip-or-tip page. This page keeps the block on an incline under its own weight.

Q: Where is the applied force?

A force parallel to the incline is on the incline-friction page. A horizontal force on the incline is on the incline-horizontal page.

Whether a homogeneous rectangle on an incline slips or tips under its own weight. The slip angle is the friction angle. The tip angle is the moment about the downhill edge. Runs locally.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary Engine tested · Source checked · 7/7 tests · Production surface contract 6/6 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
Model: Whether a homogeneous rectangle on an incline slips or tips under its own weight, and the angle at which that happens.
Scope: Calculation runs locally in the browser; values are not uploaded.
Verification: Engine tested · 7/7 tests · Production surface contract 6/6 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: Hibbeler, Engineering Mechanics: Statics — Dry friction — tipping or slipping of a block on an incline
Sources
Evidence: 3 golden · 4 boundary · Production surface contract 6/6 · Artifact integrity PASS
Production: Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (6 capabilities; 189 remain CURRENT) @ 2026-09-23T14:00:05.385Z
Semantic contract: PASS

Formulas

Core equations used by this calculator.

Sliptan θ_slip = μ

Tiptan θ_tip = b / h

ib is the base along the incline. h is the height perpendicular to the incline. The center is at the middle of the rectangle. This page does not apply an extra force, and it does not solve a wedge or a belt.

How to use

Enter μ

The coefficient at impending slip. Zero is a smooth incline.

Enter the base and the height

b lies along the incline. h is perpendicular to the incline.

Read which mode happens first

slip, tip, or either. θ is the smaller of the two critical angles.

Example calculations

Common configurations with formula and result.

Slip and tip together

μ = 1, b = 2, h = 2

θ_slip = 45°, θ_tip = 45°

either, θ = 45°

Slips first

μ = 0, b = 2, h = 2

θ_slip = 0°, θ_tip = 45°

slip, θ = 0°

Tips first

μ = 1, b = 1, h = 2

θ_slip = 45°, tan θ_tip = 1/2

tip

Incline Slip or Tip calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 7/7 tests · Production surface contract 6/6
Named expert review Not performed
Calculation version 1.0.0

Review policy · Evidence

Definition: Under its own weight, a homogeneous rectangle slips at tanθ = μ and tips at tanθ = b/h. The smaller angle happens first. Equal angles are reported as either.
What it calculates: Whether a homogeneous rectangle on an incline slips or tips under its own weight, and the angle at which that happens.
Inputs: mu
b
h
Outputs: mode
theta_deg
theta_slip_deg
theta_tip_deg
Formula: tanθ_slip = μ, tanθ_tip = b/h
Assumptions: Calculation runs locally in the browser; values are not uploaded.
Keep units consistent with the labels on each field.
b is the base along the incline. h is the height perpendicular to the incline. The center is at the middle of the rectangle. This page does not apply an extra force, and it does not solve a wedge or a belt.
Units: θ is in degrees. b and h share one length unit. μ is dimensionless.
Boundary conditions: missing μ, b, or h → MISSING_REQUIRED_INPUT
b ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE
μ < 0 → VALUE_OUT_OF_RANGE
Example: mu=1 b=2 h=2 → either, θ=45°
Validation cases: 4 published on this page · 7/7 tests · Production surface contract 6/6 · View evidence
mu=1 b=2 h=2 → mode=either, theta_deg=45
mu=0 b=2 h=2 → mode=slip, theta_deg=0
mu=1 b=1 h=2 → mode=tip, theta_slip_deg=45
mu=-0.1 b=2 h=2 → VALUE_OUT_OF_RANGE
Sources: Hibbeler, Engineering Mechanics: Statics — Dry friction — tipping or slipping of a block on an incline
Supports: Impending slip down the plane is tanθ = μ. A homogeneous rectangle tips about the downhill edge when tanθ = b/h.
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Find whether a rectangle on an incline slips or tips under its own weight.

Supported and not supported

Supported: a homogeneous rectangle of base b along the incline and height h perpendicular to it. θ_slip is the friction angle from the incline-friction engine. θ_tip is the angle where the vertical through the center passes through the downhill edge.

Not supported: a horizontal force on a level surface, an extra force along the plane, wedges, screws, and belts. /calc/mechanical is not open.

Agent / API notes

Capability id: mechanical.statics.incline_slip_or_tip · tool id: incline-slip-or-tip · pin 1.0.0.

{ "mu": 1, "b": 2, "h": 2 }

Share the link with mu, b, and h. The result is not written into the link.

Other calculators in this family: Horizontal force on an incline, Incline friction, Slip or tip, Friction .

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Frequently asked questions

Key distinctions behind the calculation.

What does either mean?