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Physics calculator

Angled Pull Calculator

Pull at an angle above the horizontal that puts a block on a level surface at impending slip. The normal is W − P sinα. 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
The pull at an angle above the horizontal that puts a block on a level surface at impending slip, and the normal and friction forces.
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 — a force applied at an angle on a level surface
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Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (6 capabilities; 189 remain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.

PullP = μ W / (cos α + μ sin α)
NormalN = W − P sin α
iα = 0 is a horizontal pull, and then P = μW. This page does not solve an incline or decide tipping.

How to use

1

Enter the weight and μ

W is in newtons. μ is the coefficient at impending slip.

2

Enter the angle

α is in degrees above the horizontal, from 0 up to but not including 90.

3

Read P, N, and F

P is the pull. F is friction and is negative because it opposes the motion. N is the normal.

Example calculations

Common configurations with formula and result.

ϟ

Horizontal pull

W = 100 N, μ = 0.25, α = 0°

P = μW
P = 25 N, N = 100 N, F = −25 N
ϟ

45° with μ = 1

W = 100 N, μ = 1, α = 45°

P = 50√2, N = 50
P = 70.710678 N, N = 50 N, F = −50 N
ϟ

Smooth surface

W = 100 N, μ = 0, α = 0°

P = 0
P = 0 N, N = 100 N

Angled Pull calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
On a level surface, a pull at angle α above the horizontal satisfies P = μW / (cosα + μ sinα). The normal is W − P sinα.
What it calculates
The pull at an angle above the horizontal that puts a block on a level surface at impending slip, and the normal and friction forces.
Inputs
  • W
  • mu
  • alpha_deg
Outputs
  • P
  • N
  • F
Formula
P = μW / (cosα + μ sinα), N = W − P sinα
Assumptions
  • Calculation runs locally in the browser; values are not uploaded.
  • Keep units consistent with the labels on each field.
  • α = 0 is a horizontal pull, and then P = μW. This page does not solve an incline or decide tipping.
Units
  • W, P, N, and F are in one force unit. α is in degrees. μ is dimensionless.
Boundary conditions
  • missing W, μ, or α → MISSING_REQUIRED_INPUT
  • W ≤ 0 → VALUE_MUST_BE_POSITIVE
  • α outside [0, 90) or μ < 0 → VALUE_OUT_OF_RANGE
Example
W=100 mu=0.25 alpha_deg=0 → P=25, N=100, F=-25
Validation cases

4 published on this page · 7/7 tests · Production surface contract 6/6 · View evidence

  • W=100 mu=0.25 alpha_deg=0 → P=25, N=100, F=-25
  • W=100 mu=1 alpha_deg=45 → P=50√2, N=50, F=-50
  • W=100 mu=0 alpha_deg=0 → P=0, N=100, F=0
  • W=100 mu=0.25 alpha_deg=90 → VALUE_OUT_OF_RANGE
Sources
  • Hibbeler, Engineering Mechanics: Statics — Dry friction — a force applied at an angle on a level surface
    Supports: Impending slip gives P cosα = μN and N + P sinα = W, so P = μW / (cosα + μ sinα).
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Find the pull at an angle that puts a block on a level surface at impending slip.

Supported and not supported

Supported: weight W, coefficient μ, and a pull at angle α above the horizontal. α = 0 is a horizontal pull. The normal is W − P sinα. The friction magnitude comes from the friction engine and opposes the motion.

Not supported: an incline, tipping, wedges, screws, and belts. /calc/mechanical is not open.

Agent / API notes

Capability id: mechanical.statics.angled_pull · tool id: angled-pull · pin 1.0.0.

{ "W": 100, "mu": 0.25, "alpha_deg": 0 }

Share the link with W, mu, and alpha_deg. The result is not written into the link.

Other calculators in this family: Angled pull on an incline, Least pull, Horizontal force on an incline, Slip or tip, Friction .

P Angled pull on an incline › P Least pull › P Horizontal force on an incline › P Slip or tip › F Friction ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this an incline?

No. The surface is level. A horizontal force on an incline is the incline-horizontal page.

Does raising the angle reduce the pull?

The angle that minimizes the pull is the least-pull page. This page reports the pull at the angle you enter.

Does this decide tipping?

No. A horizontal force at a height on a level surface is the slip-or-tip page.