Triangle Face Shape: Jaw Widest, Forehead Narrowest, Decided by Distance
A triangle face shape means the jaw is the widest of the three widths and the forehead is the narrowest, with the cheekbones in the middle. The classifier compares the three ratios with every shape's intervals and returns the shape with the smallest distance; the Triangle intervals are jaw-to-cheekbone 1.02 to 1.10, forehead-to-cheekbone 0.80 to 0.98, and length-to-cheekbone 1.00 to 1.55. The verdict is the smallest distance, not a pass on all three intervals at once. Pear names the same jaw-widest outline on this page, with no separate threshold and no separate page. Inverted triangle is not defined here; it is defined on the Heart face shape page.
The core mathematical ratios: how the distance classifier decides Triangle
Measure four straight spans in one unit: forehead width (F), cheekbone width (C), jaw width (J), and hairline-to-chin length (L). Divide J by C, F by C, and L by C to get the three ratios the classifier compares. For each interval, the violation is the distance from the ratio to the nearest bound, or 0 inside the interval. A shape distance is the mean of its three violations. The smallest distance wins, equal distances use the listed order, a next distance within 0.04 is a close call with alternatives shown, and a best distance above 0.10 is a poor fit. The Triangle jaw interval is 1.02 to 1.10, so the jaw must clear the cheekbones by more than the 0.02 clearance (self-calc: 1.02 − 1.00) built into the lower bound. The Triangle forehead interval is 0.80 to 0.98, so the forehead must sit below the cheekbones by more than the same 0.02 clearance (self-calc: 1.00 − 0.98) at the top. The Triangle length interval is 1.00 to 1.55, so the face must be at least as long as it is wide and no longer than the Diamond and Oval boundary at 1.55. Forehead-to-jaw ratio is shown for reading only as F divided by J, which equals forehead-to-cheekbone divided by jaw-to-cheekbone, and it does not enter the distance.
Controlled boundary retest: six benchmark test cases
The six rows below use synthetic fixtures, not measurements of people, and each row compares the Triangle distance with the Heart distance computed from the published Heart bounds. Heart length contributes 0 to the Heart distance in these rows because no Heart length interval is published; the live classifier's own Heart length interval governs the live verdict.
| Sample ID | Forehead (F) | Cheekbone (C) | Jaw (J) | Length (L) | J/C (self-calc: J ÷ C) | F/C (self-calc: F ÷ C) | L/C (self-calc: L ÷ C) | F/J (self-calc: F ÷ J, derived) | Triangle distance (self-calc: mean of 3 violations) | Heart distance (self-calc: mean of 3 violations) | Result | Decision Rationale |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| T1_CANONICAL | 128 mm | 140 mm | 152 mm | 185 mm | 1.086 | 0.914 | 1.321 | 0.842 | 0.0000 | 0.1598 | Triangle (close call) | Triangle distance is 0.0000 and Square distance is 0.0357, a gap of 0.0357 within 0.04, so the reading is Triangle as a close call with Square as the alternative. Heart distance is 0.1598. |
| T2_BORDERLINE_JAW | 132 mm | 140 mm | 141 mm | 188 mm | 1.007 | 0.943 | 1.343 | 0.936 | 0.0043 | 0.0927 | Triangle (close call) | Triangle distance is 0.0043 from a 1 mm jaw lead (141 − 140 mm). Runner-up is Round at 0.0333 (tied with Square at 0.0333), a gap of 0.0290 within 0.04, so the reading is Triangle as a close call with Round, Square, and Diamond (0.0357) as alternatives. Heart distance is 0.0927. |
| T3_HEART_CONTRAST | 152 mm | 142 mm | 108 mm | 190 mm | 0.761 | 1.070 | 1.338 | 1.407 | 0.1166 | 0.0000 | Heart (close call) | Heart distance is 0.0000 and runner-up Round distance is 0.0362, a gap of 0.0362 within 0.04, so the reading is Heart as a close call with Round as the alternative. Triangle distance is 0.1166, with a poor-fit flag judged on best distance (0.0000, not poor fit). |
| T4_DIAMOND_CONTRAST | 128 mm | 145 mm | 112 mm | 190 mm | 0.772 | 0.883 | 1.310 | 1.143 | 0.0825 | 0.0391 | Diamond (close call) | Diamond distance is 0.0000 and runner-up Round distance is 0.0034, a gap of 0.0034 within 0.04, with Heart at 0.0391 also within 0.04, so the reading is Diamond as a close call with Round and Heart as alternatives. Triangle distance is 0.0825. |
| T5_SQUARE_CONTRAST | 145 mm | 146 mm | 142 mm | 175 mm | 0.973 | 0.993 | 1.199 | 1.021 | 0.0202 | 0.0432 | Square (close call) | Square distance is 0.0000 and runner-up Round distance is 0.0075, a gap of 0.0075 within 0.04, with Triangle at 0.0202 also within 0.04, so the reading is Square as a close call with Round and Triangle as alternatives. Heart distance is 0.0432. |
| T6_ELONGATION_GATE | 128 mm | 140 mm | 152 mm | 224 mm | 1.086 | 0.914 | 1.600 | 0.842 | 0.0167 | 0.1598 | Oblong (close call) | Oblong distance is 0.0167 and Triangle distance is 0.0167, tied on distance. Under tie order Oblong precedes Triangle, so the reading is Oblong as a close call with Triangle (gap 0.0000) and Oval (0.0552, gap 0.0385 within 0.04) as alternatives. Heart distance is 0.1598. |
Thresholds in this table are calibrated engineering heuristics applied to standardized 2D frontal frames, for reproducible self-measurement, not an immutable clinical diagnosis.
Two meanings of triangle: bone outline and hair ends
Triangle has 2 meanings in hair and face talk, and only the first uses face measurements. Meaning 1, the bone outline, is decided by 4 inputs, F, C, J, and L, and by the 3 distances in the table above. Meaning 2, the hair-ends triangle, is decided by 0 width inputs, because it describes how layers fall at the ends, not how wide the jaw is. The test is the landmark named: jaw corners and temples mean Meaning 1, while stacked or unblended layers near the neck mean Meaning 2. One reply asks: "Triangle shape? Do you mean your layers? Genuinely can't see what you mean otherwise". A second reply in the same thread says: "my hair near my neck is so much straighter than the rest, I asked my hairdresser to make sure the layers are not stacked and are blended nicely". Neither reply names a width, a ratio, or a jaw measurement, which is how Meaning 2 is told apart from Meaning 1.
Real community dilemmas: four threads, four blocks
1. r/HairStyleAdvice
The first thread starts from the label and asks what to do next. The post asks: "i have an inverted triangle face, what haircuts could fit me?" This solves the next-step block: the label alone gives no cut, and the cut question must follow the width order, jaw widest and forehead narrowest, before any style is chosen.
2. r/Makeup101
The second thread lists 4 labels for 1 face. The post asks: "What is my face shape? Oval? Heart? Round? Upside down triangle?" This solves the naming block: 4 names from 1 person show the block is the name, not the measuring, because no width order is given in the question.
3. r/Makeup101
The third thread reports the same face judged differently years apart. The post says: "Face shape confirmation: I have always assumed I have an oval face, but with age I feel my chin is slightly less rounded". This solves the time block: a label from years ago cannot stand without new measurements, because the classifier reads the 4 current inputs, not the old label.
4. r/curlyhair
The fourth thread uses triangle for hair ends, not for bone widths. The post asks: "Help! Why does my hair ends up shaped like a triangle?" This solves the word block: the same word names 2 different checks, and the check is named by its landmark, layers at the neck or widths at the jaw.
Verifying your measurements at home
Measure F across the temples, C across the cheekbone peaks, J across the jaw corners below the ears, and L from the center of the hairline to the chin tip, all as straight spans in one unit. Enter the 4 numbers in the unit the form shows, with the same unit for all 4, and the classifier computes J divided by C, F divided by C, and L divided by C. The input calls the same distance classifier as the home page, with the Triangle intervals above as its Triangle inputs, and it adds no second rule set. The output names the verdict, the violated intervals by ratio name, the 3 ratios, and the distances, smallest first. A next distance within 0.04 adds the close-call flag and the alternatives, and a best distance above 0.10 adds the poor-fit flag. The form rejects an entry set when the largest entered value divided by the smallest exceeds 4, so mixed units or a misplaced decimal cannot return a verdict. Changing an entry clears the displayed result until the calculation is run again, and reloading the page leaves the 4 boxes blank. Test the same 4 numbers on the home-page detector at Face Shape Detector and compare the verdict name, the 3 ratios, and the distances before trusting any single label. For why different tools return different labels for the same face, see What is my face shape.
Face Shape Distance Calculator
Frequently asked questions
Q1. I have an inverted triangle face. What haircuts could fit me?
Measure the width order first. The cut follows the order, and no cut is named on this page.
Q2. What is my face shape? Oval? Heart? Round? Upside down triangle?
Enter the four widths and length and read the smallest distance. A name without numbers cannot decide it.
Q3. I always assumed oval, but my chin looks less rounded with age. What changed?
Re-measure the four current inputs. The classifier reads current numbers, not the old label.
Q4. Why does my hair ends up shaped like a triangle?
That triangle is the hair ends, not the bone outline. The test is layers at the neck, not widths at the jaw.
Sources
1.02 to 1.10 (jaw-to-cheekbone), 0.80 to 0.98 (forehead-to-cheekbone), and 1.00 to 1.55 (length-to-cheekbone) (proposed) — Triangle intervals — faceshapelens.com — checked 2026-10-30
0.02 (clearance from 1.00 to each bound, self-calc: 1.02 − 1.00 and 1.00 − 0.98); 0.04 and 0.10 (prototype choices, not validated thresholds for close-call and poor-fit margins); 3 violations averaged into one distance, violation = max(a − ratio, 0, ratio − b) — distance classifier mechanics — faceshapelens.com — checked 2026-10-30
J/C ≤ 0.85, F/C ≥ 1.00 and F/J ≥ 1.00 — published Heart bounds used for Heart distance — faceshapelens.com — checked 2026-10-30
L/C 1.30 to 1.55, J/C ≤ 0.90 and F/C ≤ 0.95 — published Diamond bounds used for Diamond distance — faceshapelens.com — checked 2026-10-30
0.95 ≤ F/C ≤ 1.05, J/C ≥ 0.95 and L/C ≤ 1.25 — published Square bounds used for Square distance — faceshapelens.com — checked 2026-10-30
L/C 1.55 to 1.65, J/C ≤ 0.92 and F/C ≤ 1.00 — published Oval bounds used for Oval distance — faceshapelens.com — checked 2026-10-30
T1 to T6 (T1: F 128 mm, C 140 mm, J 152 mm, L 185 mm, J/C 1.086, F/C 0.914, L/C 1.321, F/J 0.842, Triangle dist 0.0000, Square dist 0.0357, Heart dist 0.1598, gap 0.0357; T2: F 132 mm, C 140 mm, J 141 mm, L 188 mm, J/C 1.007, F/C 0.943, L/C 1.343, F/J 0.936, Triangle dist 0.0043, Round dist 0.0333, Heart dist 0.0927, gap 0.0290, jaw lead 1 mm; T3: F 152 mm, C 142 mm, J 108 mm, L 190 mm, J/C 0.761, F/C 1.070, L/C 1.338, F/J 1.407, Heart dist 0.0000, Round dist 0.0362, Triangle dist 0.1166, gap 0.0362; T4: F 128 mm, C 145 mm, J 112 mm, L 190 mm, J/C 0.772, F/C 0.883, L/C 1.310, F/J 1.143, Diamond dist 0.0000, Round dist 0.0034, Triangle dist 0.0825, gap 0.0034; T5: F 145 mm, C 146 mm, J 142 mm, L 175 mm, J/C 0.973, F/C 0.993, L/C 1.199, F/J 1.021, Square dist 0.0000, Round dist 0.0075, Triangle dist 0.0202, gap 0.0075; T6: F 128 mm, C 140 mm, J 152 mm, L 224 mm, J/C 1.086, F/C 0.914, L/C 1.600, F/J 0.842, Oblong dist 0.0167, Triangle dist 0.0167, tie-break to Oblong, Oval dist 0.0552, Heart dist 0.1598) — covers T1 to T6, all calculated by the shared classifier module — faceshapelens.com — checked 2026-10-30
4 (largest-divided-by-smallest entry limit); 4 boxes blank after reload; result cleared on entry change until recalculated; 2 meanings, 3 ratios, 4 inputs, 6 test rows, 4 threads, 1 verdict — form limits and article item counts — faceshapelens.com — checked 2026-10-30
r/HairStyleAdvice (22 October 2026), r/Makeup101 (3 December 2025 and 30 August 2026), r/curlyhair (11 June 2026) — posting dates of the 4 community quotes, as supplied, threads not re-opened — reddit.com — checked 2026-10-30