Cantilever Beam Deflection Calculator: equations, variables, units and worked solution

The cantilever beam deflection calculator calculates Cantilever Beam Deflection — tip deflection, Cantilever Beam Deflection — tip deflection, Fixed-end moment, Equivalent tip stiffness from Force, Length, Elastic Modulus, Inertia. It does not hide the arithmetic: the result panel shows the governing formula, canonical-unit conversion, numeric substitution, unrounded evaluation and final rounded answer for every output.

Variables and measurement units

For the Cantilever Beam Deflection Calculator, Force, Length, and Elastic Modulus are normalized to N, m, and Pa before force*length**3/(3*elasticModulus*inertia) is evaluated. The unrounded value used for force*length**3/(3*elasticModulus*inertia) and Cantilever Beam Deflection — tip deflection is retained internally; formatting is applied only to the result cards.

Formula model

For an Euler–Bernoulli cantilever with a tip load, end deflection δ = FL³/(3EI), fixed-end moment M = FL, and tip stiffness k = 3EI/L³.

Formula-based worked derivation

1. Cantilever Beam Deflection — tip deflection
   1. Formula: Cantilever Beam Deflection — tip deflection = force × length^3 ÷ (3 × elasticModulus × inertia)
   2. Default substitution: Cantilever Beam Deflection — tip deflection = (1000) × (2)^3 ÷ (3 × (200000000000) × (2e-05))
   3. Unrounded evaluation: 0.000666666666667 m
   4. Displayed answer: 0.00066667 m
2. Cantilever Beam Deflection — tip deflection
   1. Formula: Cantilever Beam Deflection — tip deflection = force × length^3 ÷ (3 × elasticModulus × inertia) × 1000
   2. Default substitution: Cantilever Beam Deflection — tip deflection = (1000) × (2)^3 ÷ (3 × (200000000000) × (2e-05)) × 1000
   3. Unrounded evaluation: 0.666666666667 mm
   4. Displayed answer: 0.6667 mm
3. Fixed-end moment
   1. Formula: Fixed-end moment = force × length
   2. Default substitution: Fixed-end moment = (1000) × (2)
   3. Unrounded evaluation: 2000 N·m
   4. Displayed answer: 2000 N·m
4. Equivalent tip stiffness
   1. Formula: Equivalent tip stiffness = 3 × elasticModulus × inertia ÷ length^3
   2. Default substitution: Equivalent tip stiffness = 3 × (200000000000) × (2e-05) ÷ (2)^3
   3. Unrounded evaluation: 1500000 N/m
   4. Displayed answer: 1500000.0 N/m

In the Cantilever Beam Deflection Calculator, changing Force, Length, and Elastic Modulus rebuilds the numeric substitution for force*length**3/(3*elasticModulus*inertia). The engine converts selected measurements to N, m, and Pa, retains unrounded values, and, when reverse solving is available, inserts the solved variable back into the same equation to verify force*length**3/(3*elasticModulus*inertia) and Cantilever Beam Deflection — tip deflection with a numerical residual.

Input and output interpretation

Use measured or documented values for Force, Length, Elastic Modulus, Inertia. The calculated outputs are Cantilever Beam Deflection — tip deflection, Cantilever Beam Deflection — tip deflection, Fixed-end moment, Equivalent tip stiffness. Check each intermediate line before relying on the final value; an implausible intermediate quantity usually identifies a unit, range or assumption error.

Algorithm and verification

The Cantilever Beam Deflection Calculator uses its own `cantilever-deflection` JavaScript engine to calculate force*length**3/(3*elasticModulus*inertia) and Cantilever Beam Deflection — tip deflection from Force, Length, and Elastic Modulus with force*length**3/(3*elasticModulus*inertia). Calculator-owned boundary and mode tests check that workflow; an external frozen-reference oracle checks the numeric outputs, and physical source mutation testing confirms that a changed `cantilever-deflection` engine is rejected.

Visual interpretation

In the Cantilever Beam Deflection Calculator, this guidance applies to Force, Length, and Elastic Modulus and the reported force*length**3/(3*elasticModulus*inertia) and Cantilever Beam Deflection — tip deflection. The `cantilever-deflection` workflow evaluates force*length**3/(3*elasticModulus*inertia) in N, m, and Pa; Confirm sign conventions, unit systems, material properties and boundary conditions before engineering use.. Verification context: 8ad23b.

Dimensional formula audit

The cantilever beam deflection calculator normalizes force (Force, N), length (Length, m), elasticModulus (Elastic Modulus, Pa), inertia (Inertia, m⁴) before evaluating the equations. Its reported quantities are Cantilever Beam Deflection — tip deflection in m, Cantilever Beam Deflection — tip deflection in mm, Fixed-end moment in N·m, Equivalent tip stiffness in N/m. This separation matters because a numerical value without its measurement dimension can produce a plausible-looking but physically or financially incorrect answer. Conversion factors are applied before substitution, and output conversion occurs only after the canonical result has been calculated at full precision.

• Cantilever Beam Deflection — tip deflection = force × length^3 ÷ (3 × elasticModulus × inertia)
• Cantilever Beam Deflection — tip deflection = force × length^3 ÷ (3 × elasticModulus × inertia) × 1000
• Fixed-end moment = force × length
• Equivalent tip stiffness = 3 × elasticModulus × inertia ÷ length^3

Formula sensitivity and boundary verification

To verify the cantilever beam deflection calculator, hold all other inputs fixed and change force within its permitted range. The live substitution line shows exactly where that value enters the equation for Cantilever Beam Deflection — tip deflection. Repeat the check with length. The result must follow the displayed algebra, remain finite, and retain the stated output unit. At minimum and maximum boundaries, the validator rejects undefined domains, impossible denominators and nonphysical values rather than silently returning a number.

Manual reproduction of the result

For an independent hand check, first convert every selected unit to the canonical units shown in the variable table. Next copy the governing equation, replace each symbol with the canonical value shown in the live derivation, and calculate the intermediate expression without early rounding. Finally round only once to the displayed precision and compare both the numerical value and unit with the calculator card. This process makes the cantilever beam deflection calculator reproducible instead of relying on an unexplained result.

Limitations

The Cantilever Beam Deflection Calculator validates the supported domain for Force, Length, and Elastic Modulus before evaluating force*length**3/(3*elasticModulus*inertia). Undefined denominators, impossible roots, non-finite values, and out-of-range selections are rejected before force*length**3/(3*elasticModulus*inertia) and Cantilever Beam Deflection — tip deflection is displayed.