Assertions

An assertion is a maths block that holds one comparison. It doesn’t compute a number; it answers true or false, and answers again every time an input changes. It’s how a calcsheet states that the design works (or doesn’t) instead of leaving the reader to compare two numbers by eye.

Assertions are available on every plan.

Write a check

Define the values, then put the comparison in a block of its own:

A sheet with two definitions and a passing check, then two more and a failing one

The third block reads $f_{d} \leq f_{y}$ and answers = true: a design stress of $180 MPa$ against a yield strength of $275 MPa$ . The last reads $d \leq d_{a}$ and answers = false: $18 mm$ of deflection against an allowable $15 mm$ .

A check is evaluated like any other block, top to bottom and left to right, so define what it compares above it. Change $f_{d}$ to $300 MPa$ and the first check flips to = false on the spot.

The six operators

Check	Type	Toolbar button
$a = b$	`==`	= (Equal to)
$a \neq = b$	`!=`	≠
$a < b$	`<`	<
$a > b$	`>`	>
$a \leq b$	`<=`	≤
$a \geq b$	`>=`	≥

The buttons sit on the Boolean & conditional tab of the maths toolbar, which appears whenever the caret is in a maths block.

The Boolean and conditional tab of the maths toolbar: if, equals, not equals, less, greater, less or equal, greater or equal, and, or, not

Typed <=, >= and != turn into $\leq$ , $\geq$ and $\neq =$ as you type. == stays as two equals signs, and so does the = button: it inserts ==.

Equal means `==`

A single = assigns. So does :=. Write n = 3 and you haven’t tested whether $n$ is 3, you’ve redefined it:

n := 3 on one line, then n == 3 answering = true on the next

This is the commonest way to lose a check: type =, get a quiet redefinition where you wanted a verdict. For equality, always ==.

Reading the result

On the page, a check shows = true or = false, like any other result. The page itself stays plain; the colour is in the sidebar.

Open the Navigate tab. Every check on the sheet is listed under Assertions, in reading order, with its status:

The Assertions section of the sidebar, listing three checks marked PASS, FAIL and ERROR

Status	Means
PASS	The comparison is true.
FAIL	The comparison is false.
ERROR	It couldn’t be evaluated.

Click an entry to jump to its block. Before you print a sheet or hand it over, scan the list for anything that isn’t green.

Whether a check shows its = true on the page follows the sheet’s Show expression evaluations by default setting (see Calcsheet options). Right-click a block and choose Hide Evaluation or Show Evaluation to override it for that block. Hiding the answer doesn’t remove the check from the list.

When a check errors

A check that can’t be evaluated shows a red message in the block and ERROR in the list. It is neither a pass nor a fail.

A check comparing a stress with a length, showing the message Cannot compare units with different base

The usual causes are a name that isn’t defined (Undefined symbol …) and a comparison between different kinds of quantity, as above. A check you can’t evaluate is a check you haven’t done.

What can be compared

Numbers and units. Units are converted before comparing, so $1 m = 100 cm$ is true and $5 m > 3 ft$ is true. Different kinds of quantity (a stress against a length) can’t be compared; that’s the error above.

Full precision, not the displayed figure. Results are rounded to the sheet’s decimal places for display, but a check compares the stored value. With $x := 0.30004$ , the result reads $0.3$ at four places, yet $x == 0.3$ is = false. Floating-point dust is forgiven: $0.1 + 0.2 == 0.3$ is = true.

Text. Two pieces of text compare as labels: exactly, and case-sensitively. "M12" == "M12" is true; "M12" == "m12" is false. Text against a number is simply false, not an error. Press “ to type text in a maths block (see Keyboard shortcuts).

Vectors and matrices. Compared element by element. The block shows a true or false for each element, and the check passes only if every one is true. With $v = (1, 2, 3)$ , $v > 0$ passes and $v > 2$ fails.

When a check isn’t a check

The rule: a check is a block that is one comparison and nothing else. If it appears under Assertions, it’s a check. If it doesn’t, it isn’t, whatever the block says.

Chained comparisons. 0 < x < 10 is read as 0 < x. Everything after the second operand is dropped, with no error, so with $x = 5$ the block 0 < x < 3 answers = true. Write two checks.
and and or conditions. (x > 0) ∧ (x < 10) evaluates and shows = true, but it has no PASS or FAIL and isn’t listed. Write two checks, or use the condition inside an if.
Assigning the answer. ok := x > 3 defines ok as true or false. That’s a useful flag, and a definition, not a check.
Comparisons inside brackets. In if(x > 0, 1, 2) the comparison belongs to the if. It doesn’t make the block a check.