Geometry: triangles, circles, polygons, solids

Triangle — side a is opposite angle A. Give any three values with at least one side. SSS and SAS use the law of cosines; ASA and AAS the law of sines. SSA can have two, one, or no solutions: with A = 30°, b = 10, a = 6 there are two triangles (B ≈ 56.4° or 123.6°), and both are shown. Results include area (Heron’s formula), heights, inradius, and circumradius.
Circles and arcs — give radius and angle, radius and chord, radius and rise, or chord and rise (R = c²/8s + s/2, handy for laying out an arched top). Shows arc length, sector and segment areas. Three points define a circle through them.
Regular polygons — from the side, circumradius, apothem, or area. For an n-sided frame each mitre is 180°/n.
Solids — cube, box, cylinder, tube, cone, frustum, sphere, hemisphere, square pyramid, and torus. Units follow your inputs; give a density to get the mass.
Coordinates — distance, midpoint, slope, line equation, intersection, and point-to-line distance. Paste polygon vertices in order for the shoelace area, perimeter, and centroid.

Share link (under the title) copies a URL that reopens this tool exactly as you have it — every tab’s inputs, with the current tab selected. Opening such a link replaces the inputs this browser had saved for the tool.

Linking to an example

Companion to chapters 9, 10 and 13 (geometry, coordinates, trigonometry) of Mathematics, Reconnected. Each input has a short parameter, and the tab comes from the # part of the address, for example /tools/geometry/?A=30&a=6&b=10#triangle (the ambiguous case) or ?solid=cone&dims=3.











Tab
Parameter
Meaning
Example




#triangle
a, b, c, A, B, C
sides and angles in degrees; side a is opposite angle A. Give three, at least one a side
a=5&b=7&c=8


#circle
r, angle, chord, rise
any two of radius, central angle, chord and rise (sagitta)
chord=900&rise=120


#circle
pts
three points for the circle through them
pts=0,0  4,0  2,3


#polygon
n, known, value
sides, which value is known (side, R, apothem, area) and its value
n=6&known=side&value=300


#solids
solid, dims
cube, box, cylinder, tube, cone, frustum, sphere, hemisphere, pyramid, torus, and its dimensions in the order the tab lists them
solid=cylinder&dims=3.5,10


#solids
density
kg/m³, for the mass
density=750


#coords
P, Q, R, S, T
points x, y: line PQ, its intersection with RS, and T’s distance from PQ
P=1,1&Q=3,4&T=7,10


#coords
poly
polygon vertices x y, separated by |
poly=0 0|4 0|4 3



example
one of the presets below (it also picks the tab); other parameters override it
example=ch13-river




Presets:




ch09-pythagoras — Right triangle with legs 3 and 4: c = 5


ch09-ladder — A 5 m ladder 1.4 m from the wall reaches 4.8 m


ch09-ssa — SSA is ambiguous: ∠A = 30°, AB = 10, BC = 6 gives two triangles


ch09-shoelace — Shoelace area of (1,1), (5,2), (4,5), (2,4): 9


ch09-soup-can — The soup can: cylinder r = 3.5, h = 10 cm


ch09-ice-cream-cone — An ice-cream cone: r = 3, h = 12 cm, V = 36π


ch09-cylinder-3-12 — The cylinder that three of those cones fill: V = 108π


ch09-ball — A ball of radius 6 cm


ch10-collinear — Are (1, 1), (3, 4), (7, 10) collinear? T is 0 from line PQ


ch13-river — The river: baseline 500 m, angles 52° and 71° (ASA)


ch13-cosines-5-7-8 — Sides 5, 7, 8: the angle opposite 7 is 60°


ch13-navigation — 20 km then 30 km with a 110° turn angle: distance from port (SAS)


ch13-ssa — The ambiguous case: A = 30°, a = 6, b = 10, B ≈ 56.4° or 123.6°

Sharing

Linking to an example