How do you tell when the yield curve has inverted?

The yield curve surface labels the real curve inverted when the 30-year Treasury yield is more than 0.1 percentage points below the 1-month yield; on the 2026-09-22 curve the 30-year was 5.29 percent and the 1-month 3.97, so the read was upward. The same rule labels the curve upward above plus 0.1 points and flat in between, and it is applied to every day in the file.

Textbook mode, not the live curve: a synthetic Nelson-Siegel inversion. The real 2026-09-22 curve read upward.

The badge tests only the two endpoints#

A yield curve is the interest rate for lending to the Treasury over different lengths of time, drawn as a line from the shortest maturity to the longest. Normally it slopes up, because longer loans cost more. An inversion is the line tipping the other way, with short rates above long rates, and it is the shape everyone calls a recession warning. The surface draws that line for every day in its window and stacks the days along a second axis, so the curve becomes a sheet you can scrub through time and watch tilt.

The label on the page comes from one subtraction. The tool takes the last yield in the curve minus the first, which on the real data is the 30-year minus the 1-month, and thresholds it at a tenth of a point either side of zero. Above plus 0.1 the badge says upward; below minus 0.1 it says inverted; in between it says flat. A separate chip reports the day-over-day move in the 2s10s spread, the 10-year minus the 2-year, and a spread clock panel below the surface draws that pair over the same sixty sessions and over its full history.

Publish only dates with all eleven yields#

The real curve is eleven FRED constant-maturity series: 1-month, 3-month, 6-month, 1-year, 2-year, 3-year, 5-year, 7-year, 10-year, 20-year and 30-year. A scheduled job runs daily, requests the 120 newest observations for each series, joins them on date, and keeps only the dates where all eleven have a value, oldest first. It publishes the 60 most recent complete curves as one file and refuses to publish at all if fewer than 5 survive the join, so a partial fetch cannot replace a good file with a thin one. The page reads that file; the browser never calls FRED.

On the file I read while writing this, the 60 curves ran from 2026-06-29 to 2026-09-22. The latest one, in percent from short to long, was 3.97, 4.16, 4.26, 4.43, 4.71, 4.81, 4.83, 4.89, 4.96, 5.33 and 5.29. The 2-year at 4.71 and the 10-year at 4.96 put the 2s10s spread at plus 0.25 points, against plus 0.28 on the first day of the window. The 20-year at 5.33 sat above the 30-year at 5.29, a small kink at the long end that a badge computed from the endpoints alone will never mention.

Sixty sessions is the surface's window, not the page's#

Sixty complete sessions is about three months, so the sheet and its badge can show the curve steepening or flattening within a quarter and nothing older. Below the surface, the spread clock panel draws the 2s10s spread's daily history back to 1976 from a separate baked series, with recession months shaded, and that panel is where to look for when the spread last went negative. The page shades recessions but computes no lead time from inversion to downturn and no hit rate, because the tool draws yields and does not forecast from them.

The label is a rule about two endpoints, so a curve that is inverted in the middle and upward at the ends reads as upward. And the real and synthetic modes use different maturity grids, eleven points from one month on the real data and ten points from three months on the textbook curve, so a number read off one mode should not be quoted against the other.

The textbook mode inverts on purpose#

When the real curve is not inverted, which it was not on 2026-09-22, the page still needs to show what an inversion looks like forming. The synthetic mode does that with the Nelson-Siegel three-factor formula: a level, a slope factor, a curvature factor, and a decay constant. Six named presets set those four numbers for normal, flat, inverted, steepening, bear-flattening and level-shift shapes, and a transition interpolates from one preset to another over 24 to 90 frames with up to 15 basis points of seeded jitter so the sheet does not look machined. Going from the normal preset to the inverted one moves the slope factor from minus 1.6 to plus 1.6, the level from 4.0 to 3.4, and the curvature from 0 to minus 0.4, with the decay constant held at 2.0.

The deep link in the post that built the five surfaces opens the synthetic mode on its last frame, fully inverted, and the badge says so. The real mode opens on the newest curve in the published file, and the tool's rule applied to the 2026-09-22 curve gives upward. Both are labeled, and the label is the first line to read before the shape.

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Related:

• Rendering an options Greeks surface in 3D in the browser, how this surface and the other four were built on one math-to-mesh boundary
• How do you read a 3D option Greeks surface?, the companion page for the options surface