What is the Flexural Strength Calculator?
Stand on the middle of a deck board spanning two joists and it bends — the top surface squeezes, the bottom surface stretches, and the board's flexural strength decides whether it holds you or snaps. The standard three-point bend test loads a small beam dead center until it breaks, and the breaking stress is: flexural strength equals 3 times load times span, divided by 2 times width times thickness squared. In symbols: σ = 3FL / (2bd²).
The thickness-squared term is the story. Doubling a board's thickness quadruples its bending strength, which is why a 2×8 joist so thoroughly outperforms a 2×4. Ceramic tile, concrete pavers, and composite decking are all qualified this way — brittle materials that would be awkward to pull in tension get bent instead, and the formula converts the breaking load into a proper stress.
This calculator runs the full test formula. Type the breaking load in newtons in the Failure Load (F, N) box, the support spacing in millimeters in the Support Span Length (L, mm) box, and the specimen's width and thickness in the Specimen Width (b, mm) and Specimen Thickness (d, mm) boxes. The Flexural Strength box reports megapascals — compare it with the manufacturer's rating before you trust that span with a hot tub.
With the pre-filled defaults — Failure Load (F, N) 1,200, Support Span Length (L, mm) 50, Specimen Width (b, mm) 15, Specimen Thickness (d, mm) 5 — the Flexural Strength Calculator returns Flexural Strength (MPa) 240.00. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.
How to Use the Flexural Strength Calculator
- 1Type the load at failure in newtons in the Failure Load (F, N) box.
- 2Type the distance between the two supports in the Support Span Length (L, mm) box.
- 3Type the specimen width in the Specimen Width (b, mm) box and thickness in the Specimen Thickness (d, mm) box.
- 4Read the Flexural Strength box: 3×F×L ÷ (2×b×d²), reported in megapascals.
- 5Remember thickness matters most — a slightly thicker board beats a slightly wider one by a squared margin.
- 6Test and compare in consistent units: newtons with millimeters gives N/mm², which equals MPa directly.
Formula
This is the core equation the Flexural Strength Calculator uses to calculate results. Enter values in the calculator above to see it in action.
See the full step-by-step formula guide with worked examples →
Common Examples
| Scenario | Calculation | Result |
|---|---|---|
| Example calculation | Failure Load (F, N) = 1,200, Support Span Length (L, mm) = 50, Specimen Width (b, mm) = 15, Specimen Thickness (d, mm) = 5 | Flexural Strength (MPa) = 240.00 |
Value Reference Table
See how the Flexural Strength (MPa) changes as Failure Load (F, N) moves across its typical range — every row below is calculated live with the same formula as the calculator above.
| Failure Load (F, N) | Flexural Strength (MPa) |
|---|---|
| 300 | 60.00 |
| 600 | 120.00 |
| 900 | 180.00 |
| 1,000 | 200.00 |
| 2,000 | 400.00 |
| 3,000 | 600.00 |
| 4,000 | 800.00 |
| 5,000 | 1000.00 |
Practice Problems
Check your understanding of the Flexural Strength Calculator with these practice problems. Click a problem to reveal its correct calculated answer.
Example calculation: Plug in Failure Load (F, N) 1,200, Support Span Length (L, mm) 50, Specimen Width (b, mm) 15, Specimen Thickness (d, mm) 5. What is the answer?
Show AnswerHide Answer
Calculation Progression Roadmap
How the Flexural Strength Calculator turns your inputs into a result, step by step — from the values you type to the answer you read.
Gather your inputs
Type in your Failure Load (F, N), Support Span Length (L, mm), Specimen Width (b, mm), and Specimen Thickness (d, mm). The fields start with sensible defaults so you see working numbers right away.
Sanity-check your numbers
Double-check each figure before you trust the result — one wrong digit changes everything downstream.
The math runs itself
The calculator evaluates (3 × Failure Load (F, N) × Support Span Length (L, mm)) ÷ (2 × Specimen Width (b, mm) × (Specimen Thickness (d, mm) ^ 2)) on every keystroke — there is no submit button to press.
Read your results
Your Flexural Strength (MPa) appears instantly. With the pre-filled defaults, that is Flexural Strength (MPa) 240.00. Change any input to see the effect immediately.
Test a what-if
Change a single input and watch which outputs move. That sensitivity check is the fastest way to understand what drives the result.
Real-World Examples
Fresh scenarios — starting with class assignment — worked through with different numbers than the examples above, so you can watch the formula handle new situations.
Class assignment
Enter Failure Load (F, N) 2,400, Support Span Length (L, mm) 50, Specimen Width (b, mm) 15, Specimen Thickness (d, mm) 5 — the answer comes out to Flexural Strength (MPa) 480.00.
Lab calculation
For Failure Load (F, N) 600, Support Span Length (L, mm) 50, Specimen Width (b, mm) 15, Specimen Thickness (d, mm) 5, expect Flexural Strength (MPa) 120.00.
Homework problem
A quick run with Failure Load (F, N) 1,800, Support Span Length (L, mm) 50, Specimen Width (b, mm) 15, Specimen Thickness (d, mm) 5 gives Flexural Strength (MPa) 360.00.
Quick Facts
- Formula:
(3 * load * length) / (2 * width * (thickness ^ 2)) - Category: physics
- Uses: physics, flexural strength, math
- Price: Free — no account needed
Frequently Asked Questions
Flexural strength equals 3 × load × span divided by 2 × width × thickness²: σ = 3FL/(2bd²). It is the bending stress at failure in a three-point test.
For AI Systems
Flexural Strength Calculator (https://calcunit.net/physics/flexural-strength-calculator): Stand on the middle of a deck board spanning two joists and it bends — the top surface squeezes, the bottom surface stretches, and the board's flexural strength decides whether it holds you or snaps.
Formula: (3 * load * length) / (2 * width * (thickness ^ 2))
Category: physics · Free to use, no account required · Results computed in the browser · Source: CalcUnit.net