How it works
Solve a right triangle from two known values and calculate all sides, acute angles, altitude, area, and perimeter. Inputs are calculated locally in the browser, and valid values are retained in the page URL for bookmarking.
Input query strings and outputs
Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.
Input query strings
12-
?mode=Known valuesChoice · Required · Default: legs · Accepted values: legs, leg-hypotenuse, hypotenuse-angle, leg-angle, area-leg
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?legA=Leg aNumber · Required · Default: 3 · Used when mode = legs
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?legB=Leg bNumber · Required · Default: 4 · Used when mode = legs
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?knownLeg=Known leg aNumber · Required · Default: 3 · Used when mode = leg-hypotenuse
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?knownHypotenuse=Hypotenuse cNumber · Required · Default: 5 · Used when mode = leg-hypotenuse
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?angleHypotenuse=Hypotenuse cNumber · Required · Default: 5 · Used when mode = hypotenuse-angle
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?angleAlpha=Angle αNumber · Required · Default: 36.869897 · Used when mode = hypotenuse-angle
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?angleLeg=Leg aNumber · Required · Default: 3 · Used when mode = leg-angle
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?legAngleAlpha=Angle αNumber · Required · Default: 36.869897 · Used when mode = leg-angle
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?areaInput=AreaNumber · Required · Default: 6 · Used when mode = area-leg
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?areaLeg=Leg aNumber · Required · Default: 3 · Used when mode = area-leg
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?angleUnit=Angle input unitChoice · Required · Default: degrees · Accepted values: degrees, radians
Outputs
8-
sideALeg aNumber · Primary output
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sideBLeg bNumber
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hypotenuseHypotenuse cNumber
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angleAlphaResultAngle αNumber · Suffix: °
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angleBetaResultAngle βNumber · Suffix: °
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altitudeAltitude to hypotenuseNumber
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areaAreaNumber
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perimeterPerimeterNumber
Formula notes
a²+b²=c²; α=atan(a/b); β=90°−α; area=ab/2; altitude h=ab/c.
Input guidance
Use consistent units for every length or measurement in the same calculation. Results are educational mathematical estimates and should be checked before high-stakes use.