akunk Formula Check · prototype · October 2026

Formula Check

This is a 1953 scan. Press play.

We read the equation from a scanned page, turned it into math a screen reader understands, and checked it. You hear the speech a screen reader with MathCAT gives a blind engineering student.

Voice

Samantha US Daniel UK Karen AU Moira IE

Speed

1× 1.5× 2× screen-reader pace

Scanned formula. Equation 140: p sub 2 over p sub t 1 equals 2 gamma M sub 1 squared sine squared theta minus the quantity gamma minus 1, over gamma plus 1, times the bracket 2 over the quantity gamma minus 1 times M sub 1 squared plus 2, to the power gamma over gamma minus 1; which equals 7 M sub 1 squared sine squared theta minus 1, over 6, times 5 over M sub 1 squared plus 5, to the power 7 halves — NACA Report 1135 (1953), page 621, equation 140 · oblique shock waves

ResultVerified · confidence 0.983

2 lines; line 1; the fraction with numerator; p sub 2; and denominator p sub t sub 1, end sub; is equal to; the fraction with numerator; 2 gamma cap m sub 1, squared, sine squared of theta; minus, open paren gamma minus 1, close paren; and denominator open paren gamma plus 1, close paren; times; open bracket; the fraction with numerator 2; and denominator open paren gamma minus 1, close paren; times cap m sub 1, squared; plus 2; close bracket raised to the fraction with numerator gamma; and denominator gamma minus 1; power; line 2; is equal to; the fraction with numerator; 7 cap m sub 1, squared, sine squared of theta; minus 1; and denominator 6; times; open paren; the fraction with numerator 5; and denominator cap m sub 1, squared, plus 5; close paren raised to the 7 divided by 2 power

$Rendering of the recognized equation 140, identical to the scan$

Speech checks passed. No person needed to look at this one.

Now find the mistake

Same report, equation 132. The machine read almost everything correctly. Compare the two, then press the button.

Scanned formula. Equation 132: M sub 2 squared equals a fraction of (gamma plus 1) squared M sub 1 to the fourth sine squared theta, minus 4 times two factors, over the product of two brackets; which equals a second fraction in M sub 1 and theta — Original scan

Rendering of the recognized equation 132 — What the machine read

0 errorsfound by veraPDF in a PDF/UA file we built from the 1953 scan (PDF/UA-1 and WCAG 2.2 machine checks)

36 of 59formulas in two pages of that scan were misread, mostly subscripts and exponents

12 of 105formulas flagged in typeset course PDFs; both real errors were among them

How it works

You upload a whole document, not single formulas. Students keep their own screen reader; we make sure the file it reads is right.

1UploadA PDF, a scan or a Word file, or a version a vendor or an AI tool already fixed.
2Find and readEvery formula on every page becomes LaTeX and MathML.
3Speak and brailleThe speech and the Nemeth or UEB braille a screen reader will produce.
4CompareEach formula is checked against the scan and its speech; doubtful ones are flagged.Our check
5Review flagsA person looks only at flagged formulas, with the evidence beside each one.Our check
6ExportAn accessible PDF, web page or braille file, plus a record of what was checked.

More from the same report

Two formulas that passed and four that our check sent to a person. Open one to compare and listen.

VerifiedMatches the scan.

Scanned formula: q over p equals gamma over 2 times V over a sub t squared, times the quantity 1 minus gamma minus 1 over 2 times V over a sub t squared, to the minus 1 — Original scan · NACA 1135, page 6

Rendering of the recognized formula — What the machine read

What a screen reader says

q over p is equal to; gamma over 2 times; open paren; the fraction with numerator cap v; and denominator eigh sub t; close paren squared; times; open bracket; 1 minus; the fraction with numerator; gamma minus 1; and denominator 2; times; open paren; the fraction with numerator cap v; and denominator eigh sub t; close paren squared; close bracket to the negative 1 power

No flags · confidence 0.983

VerifiedMatches the scan. The equation number is kept out of the speech.

Scanned formula: gamma equals n plus 2 over n, equation 15 — Original scan · NACA 1135, page 4

What a screen reader says

gamma is equal to; the fraction with numerator; n plus 2; and denominator n

No flags · confidence 0.993

Needs reviewSubscript t was read as the Greek letter iota (ι), and one exponent 2 was dropped.

Scanned formula: T over T sub t equals 1 minus gamma minus 1 over 2 times V over a sub t squared, equals 1 minus one fifth V over a sub t squared — Original scan · NACA 1135, page 6

What a screen reader says

the fraction with numerator cap t; and denominator cap t sub iota; is equal to; 1 minus; the fraction with numerator; gamma minus 1; and denominator 2; times; open paren; the fraction with numerator cap v; and denominator eigh sub iota; close paren; is equal to; 1 minus; 1 fifth times; open paren; the fraction with numerator cap v; and denominator eigh sub iota; close paren squared

Flagged by confidence and speech check · confidence 0.972

Needs reviewEvery square was read as a dotless i: “to the ı-th power”.

Scanned formula: V over V sub m squared equals gamma minus 1 over 2 M squared times the quantity 1 plus gamma minus 1 over 2 M squared, to the minus 1 — Original scan · NACA 1135, page 6

What a screen reader says

open paren; the fraction with numerator cap v; and denominator cap v sub m; close paren to the ı-th power; is equal to; the fraction with numerator; gamma minus 1; and denominator 2; cap m to the ı-th power, times; open paren; 1 plus; the fraction with numerator; gamma minus 1; and denominator 2; cap m to the ı-th power; close paren to the ı-th power

Flagged by confidence and speech check · confidence 0.900

Needs reviewa-star (a*) is read as “a sub times”.

Scanned formula: V over a sub t squared equals 2 over gamma plus 1 times V over a star squared, equals 5 sixths V over a star squared — Original scan · NACA 1135, page 6

What a screen reader says

open paren; the fraction with numerator cap v; and denominator eigh sub t; close paren squared; is equal to; the fraction with numerator 2; and denominator gamma plus 1; times; open paren; the fraction with numerator cap v; and denominator eigh sub times end sub; close paren squared; is equal to; 5 sixths times; open paren; the fraction with numerator cap v; and denominator eigh sub times end sub; close paren squared

Flagged by confidence and speech check · confidence 0.946

Needs reviewThe formula is right, the speech is not: the denominator is read as “1 0” instead of “ten”.

Scanned formula: equals 7 over 10 M squared times the quantity 1 plus M squared over 5, to the minus 7 halves — Original scan · NACA 1135, page 6

What a screen reader says

is equal to; the fraction with numerator 7; and denominator 1 0; cap m squared times; open paren; 1 plus, the fraction with numerator; cap m squared; and denominator 5; close paren raised to the negative 7 halves power

Flagged by speech check · confidence 0.984

What we measured

Three public PDFs, six pages, 164 formulas, October 2026.

	Typeset course PDFs	1953 scanned report
Formulas read correctly	103 of 105	23 of 59
Flagged for review	12 of 105	54 of 59
Errors missed by the flags	0	2 minor
Review time vs. manual remediation	about 15%	about 50%

Flags in this table come from recognition confidence alone; the examples above add simple rule-based speech checks. Review time is an estimate from per-formula timings we assumed, not a timed study. The equations at the top come from a different page of the same report and are not part of these counts. Figures and tables were not tested.