Input Coordinates
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Multi-Point Distance
Calculate straight-line distance between two points, or total traverse distance along multiple waypoints.
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Find Destination Point
Given a starting point, bearing, and distance — find the destination coordinates.
0° = North, 90° = East, 180° = South, 270° = West
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Midpoint & Section Formula
Section Formula — divide AB in ratio m:n
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Triangle from 3 Points
Enter three vertices to compute area, perimeter, side lengths, bearings, centroid and more.
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Bearing & Distance — Formula Reference
🧭 True Bearing
θ = atan2(ΔX, ΔY)
Bearing = (θ × 180/π + 360) mod 360
Bearing = (θ × 180/π + 360) mod 360
Clockwise from North (0°–360°). ΔX = X₂–X₁, ΔY = Y₂–Y₁
↩ Back Bearing
Back = (Forward + 180) mod 360
Reverse bearing from B to A. Always 180° opposite the forward bearing.
📏 Euclidean Distance
d = √[(X₂−X₁)² + (Y₂−Y₁)²]
Straight-line distance between two Cartesian coordinate points.
⚡ Midpoint
M = ((X₁+X₂)/2, (Y₁+Y₂)/2)
Point exactly halfway between A and B on the line segment.
✂ Section Formula (Internal)
P = ((mX₂+nX₁)/(m+n),
(mY₂+nY₁)/(m+n))
(mY₂+nY₁)/(m+n))
Divides AB internally in ratio m:n from A.
✂ Section Formula (External)
P = ((mX₂−nX₁)/(m−n),
(mY₂−nY₁)/(m−n))
(mY₂−nY₁)/(m−n))
Divides AB externally in ratio m:n. m ≠ n.
📍 Destination Point
X₂ = X₁ + d·sin(θ)
Y₂ = Y₁ + d·cos(θ)
Y₂ = Y₁ + d·cos(θ)
θ in radians. Gives arrival coordinate from start + bearing + distance.
△ Triangle Area (Shoelace)
A = ½|X₁(Y₂−Y₃) + X₂(Y₃−Y₁)
+ X₃(Y₁−Y₂)|
+ X₃(Y₁−Y₂)|
Works for any triangle given three vertex coordinates. Always positive.
◎ Centroid
G = ((X₁+X₂+X₃)/3,
(Y₁+Y₂+Y₃)/3)
(Y₁+Y₂+Y₃)/3)
Point of intersection of medians. Centre of mass of triangle.
🔺 Interior Angle
cos(A) = (b²+c²−a²) / (2bc)
A = arccos(result)
A = arccos(result)
Law of cosines. a, b, c are side lengths opposite their respective vertices.
🗺 DMS Conversion
D = floor(angle)
M = floor((angle−D)×60)
S = ((angle−D)×60−M)×60
M = floor((angle−D)×60)
S = ((angle−D)×60−M)×60
Converts decimal degrees to Degrees Minutes Seconds notation.
🌐 Quadrant Rule
NE: 0°–90° SE: 90°–180°
SW: 180°–270° NW: 270°–360°
SW: 180°–270° NW: 270°–360°
True bearing quadrant classification by compass direction.
