HomeCalculatorsPhysicsHorizontal Force on an Incline Calculator
Physics calculator

Horizontal Force on an Incline Calculator

Horizontal force that puts a block on an incline at impending slip. P is positive toward the uphill side. The normal grows by P sinθ. 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 horizontal force that puts a block on an incline 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 horizontal force on an inclined block
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Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (6 capabilities; 189 remain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.

NormalN = W cos θ + P sin θ
Along the planeP cos θ + F = W sin θ
iF is μN and points down the plane when direction is up. This page does not take a force parallel to the plane, and it does not decide tipping.

How to use

1

Enter the weight, the angle, and μ

W is in newtons. θ is in degrees, from 0 up to but not including 90. μ is the coefficient at impending slip.

2

Choose the direction

up is impending motion up the plane, so friction acts down. down is the opposite.

3

Read P, N, and F

P is horizontal. Positive P points toward the uphill side. F is positive up the plane.

Example calculations

Common configurations with formula and result.

ϟ

Level surface, impending up

W = 100 N, θ = 0°, μ = 0.25, direction = up

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

Level surface, impending down

W = 100 N, θ = 0°, μ = 0.25, direction = down

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

Smooth 45° incline

W = 100 N, θ = 45°, μ = 0, direction = up

P = W, N = W√2
P = 100 N

Horizontal Force on an Incline calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
A horizontal force P, positive toward the uphill side, puts the block at impending slip. N = W cosθ + P sinθ. Friction opposes the stated direction along the plane.
What it calculates
The horizontal force that puts a block on an incline at impending slip, and the normal and friction forces.
Inputs
  • W
  • theta_deg
  • mu
  • direction
Outputs
  • P
  • N
  • F
  • direction
Formula
N = W cosθ + P sinθ, P cosθ + F = W sinθ
Assumptions
  • Calculation runs locally in the browser; values are not uploaded.
  • Keep units consistent with the labels on each field.
  • F is μN and points down the plane when direction is up. This page does not take a force parallel to the plane, and it does not decide tipping.
Units
  • W, P, N, and F are in one force unit. θ is in degrees. μ is dimensionless.
Boundary conditions
  • missing W, θ, μ, or direction → MISSING_REQUIRED_INPUT
  • W ≤ 0 → VALUE_MUST_BE_POSITIVE
  • θ outside [0, 90) or μ < 0 → VALUE_OUT_OF_RANGE
  • direction other than up or down → INVALID_INPUT
Example
W=100 theta_deg=0 mu=0.25 direction=up → 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 theta_deg=0 mu=0.25 direction=up → P=25, N=100, F=-25
  • W=100 theta_deg=0 mu=0.25 direction=down → P=-25, N=100, F=25
  • W=100 theta_deg=45 mu=0 direction=up → P=100, F=0
  • W=100 theta_deg=90 mu=0.25 direction=up → VALUE_OUT_OF_RANGE
Sources
  • Hibbeler, Engineering Mechanics: Statics — Dry friction — a horizontal force on an inclined block
    Supports: A horizontal force resolves into P cosθ along the plane and P sinθ into the surface. Impending slip sets the friction magnitude to μN.
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Find the horizontal force that puts a block on an incline at impending slip.

Supported and not supported

Supported: weight W, incline angle θ, coefficient μ, and impending motion up or down the plane. P is horizontal and positive toward the uphill side. The normal is W cosθ + P sinθ. The friction magnitude comes from the friction engine.

Not supported: a force parallel to the plane, tipping, wedges, screws, and belts. /calc/mechanical is not open.

Agent / API notes

Capability id: mechanical.statics.incline_horizontal · tool id: incline-horizontal · pin 1.0.0.

{ "W": 100, "theta_deg": 0, "mu": 0.25, "direction": "up" }

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

Other calculators in this family: Angled pull on an incline, Angled pull, Incline friction, Incline slip or tip, Friction .

P Angled pull on an incline › P Angled pull › P Incline friction › θ Incline slip or tip › F Friction ›
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Frequently asked questions

Key distinctions behind the calculation.

Is the force parallel to the incline?

No. That case is the incline-friction page. Here the force is horizontal, so it also changes the normal.

Does this decide tipping?

No. A rectangle under its own weight is the incline slip-or-tip page. A horizontal force on a level surface is the slip-or-tip page.

Which way is positive P?

Toward the uphill side. On a level surface that is the direction called up, and down returns the opposite sign.