Physics calculator

Shear and Moment Calculator

Shear and bending moment at a cut in a simply supported span. Point forces and concentrated moments only. Runs locally. Not beam deflection.

Instant result

Result

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Enter values to calculate.

Inputs—

Mode—

Formula—

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

Input interpretation: Enter values to calculate.
Result: —
Model: Support reactions and the shear and bending moment at one cut of a simply supported span.
Scope: Calculation runs locally in the browser; values are not uploaded.
Verification: Engine tested · 6/6 tests · Production surface contract 6/6 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: Hibbeler, Engineering Mechanics: Statics — Internal loadings
Sources
Evidence: 2 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Production: Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (3 capabilities; 189 remain CURRENT) @ 2026-09-23T10:40:38.140Z
Semantic contract: PASS

Formulas

Core equations used by this calculator.

ReactionsAy + By + ΣFy = 0, By L + Σ(Fy x) + ΣM = 0

SectionV and M balance the left side of the cut

iA load exactly at the cut stays on the right. This page does not integrate a distributed load and does not compute deflection.

How to use

Enter the span and the section

L is the distance between supports. s is measured from the left support and must lie strictly between them.

Enter point forces as Fy, x

Upward is positive. x is measured from the left support.

Read V and M on the left face

CCW moment is positive. Ay and By are the support reactions.

Example calculations

Common configurations with formula and result.

Downward 10 N at midspan

L = 4 m, section at 1 m

Ay = By = 5 N

V = −5 N, M = 5 N·m

Section at the load

The 10 N load stays on the right of s = 2 m

M = P L / 4

M = 10 N·m

Shear and Moment calculator specification

Version 1.0.0 · Engine tested

Calculation status

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

Review policy · Evidence

Definition: Vertical reactions of a simple span, then the shear and bending moment on the left face of a cut. Upward force and CCW moment are positive.
What it calculates: Support reactions and the shear and bending moment at one cut of a simply supported span.
Inputs: L
s
forces?
moments?
Outputs: Ay
By
V
M
Formula: ΣFy = 0 and ΣM about the left support = 0, then the left-face V and M
Assumptions: Calculation runs locally in the browser; values are not uploaded.
Keep units consistent with the labels on each field.
A load exactly at the cut stays on the right. This page does not integrate a distributed load and does not compute deflection.
Units: Length in m, force in N, moment in N·m. Upward and CCW are positive.
Boundary conditions: missing L or s → MISSING_REQUIRED_INPUT
L ≤ 0 → VALUE_MUST_BE_POSITIVE
s outside (0, L) → VALUE_OUT_OF_RANGE
a load outside the span → INVALID_INPUT
Example: L=4, s=1, forces=-10,2 → V=-5 N, M=5 N·m
Validation cases: 3 published on this page · 6/6 tests · Production surface contract 6/6 · View evidence
L=4 s=1 forces=-10,2 → Ay=5, By=5, V=-5, M=5
L=4 s=2 forces=-10,2 → V=-5, M=10
L=4 s=4 forces=-10,2 → VALUE_OUT_OF_RANGE
Sources: Hibbeler, Engineering Mechanics: Statics — Internal loadings
Supports: Shear and bending moment from equilibrium of a cut segment
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Find the shear and bending moment at one cut of a simply supported span.

Supported and not supported

Supported: point forces, concentrated moments, the two vertical reactions, and V and M on the left face of the cut.

Not supported: distributed loads, beam deflection, and indeterminate supports. /calc/mechanical is not open.

Other calculators in this family: Planar equilibrium, Principal moments .

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Frequently asked questions

Key distinctions behind the calculation.

Does this compute deflection?

No. It returns the shear and bending moment at one cut, plus the two vertical reactions. Slope, deflection, and distributed loads are out of scope.

What does a negative shear mean?

Upward force is positive. V is the vertical force on the left face of the cut. For a downward midspan load, V is negative to the left of the load and positive to the right.