Gann Calculator: The Math, the Accuracy, and What to Verify

Gann calculators produce price and time targets from anchor points using the Square of Nine geometry and related methods. The outputs look precise, specific price levels to two decimal places, specific dates marked as significant. That precision can be misleading if the underlying calculation is wrong.

This guide covers what a Gann calculator is actually computing, where popular implementations differ, and how to verify that the numbers you're working with are correct.

The core calculation: square root relationship

The fundamental Gann price calculation relies on the square root property of the Square of Nine spiral.

For any price P, the angular position on the Square of Nine is approximately:

angle = (sqrt(P) - 1) × 180°  mod 360°

The target price levels at the cardinal and diagonal angles are:

P_target = ((sqrt(P) + n/4))^2

where n = 1, 2, 3, 4, ... gives the 90°, 180°, 270°, 360° targets; n = 0.5, 1.5, ... gives the 45°, 135°, 225°, 315° targets.

This is the core Gann square root formula. Different implementations handle the rounding and the starting convention differently, which produces meaningfully different output.

The starting value problem: Some calculators start the spiral at 1 in the centre, others at 0, others at 2. This shifts every calculated level by sqrt(n) steps, changing all targets. The traditional Gann Square of Nine typically starts at 1.

The offset problem: Gann's original tables had a specific starting point for the spiral that is not always reproduced correctly in software. Some calculators apply an offset of 0.5 to the square root before computing the angle. This small difference produces targets that differ from the "standard" Gann values by several price points.

The time calculation

Gann's time projections from the Square of Nine use the same geometry applied to calendar periods.

For a major turning point on date D with calendar value C, the 90° time projection is:

days_to_next_90 = ((sqrt(C) + 0.25))^2 - C

The "calendar value" used in Gann's original work was the day of year (1-365). Some modern implementations use the number of calendar days since an arbitrary starting date (often January 1, 1900). This difference changes every time projection.

The practical consequence: two different Gann calculators, given the same anchor point, will often produce dates that differ by several days. Neither may be "wrong" in the sense of mathematical error, they're using different conventions for what calendar value to assign to the anchor date.

Angle calibration

Gann analysed different instruments at different "vibration" rates. Grains typically used 1/8-point units per degree of arc; stocks used different scales; commodities differed again.

If a calculator doesn't let you set the scale calibration for the specific instrument you're analysing, it's applying a default that may not be appropriate. Gann himself was explicit that the same instrument should show consistent turning points at the same angular levels when the scale is correctly calibrated.

Calibration is typically found empirically: take five to ten confirmed major turning points, compute the Square of Nine angles for each, and find the scale that produces the most clustering at the cardinal/diagonal angles. A well-calibrated instrument shows clear clustering at 0°, 90°, 180°, 270°.

Crohamhurst.app includes automatic scale calibration for uploaded price series, it finds the square root scale that maximises turning-point clustering at Gann angles.

What to verify in any Gann calculator

1. Square root convention: Ask the developer or test manually. Take a known price (e.g., 100). The 90° projection should be ((sqrt(100) + 0.25))^2 = (10.25)^2 = 105.06. If the calculator gives you a significantly different number for this basic case, the convention differs.

2. Calendar convention: Take a known date (e.g., January 1, 2025). Compute the 90° time projection. Different calculators will give different answers depending on their calendar anchoring. There is no single "correct" convention, but consistency within a body of analysis is required.

3. Degree resolution: Gann's primary angles are the 8-fold divisions of the circle (0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°) and the 16-fold divisions. Some calculators offer 32-fold or 64-fold divisions as well. More divisions produce more target levels, which increases the chance of apparently "hitting" a target just by density. Stick to the primary 8-fold division for the most robust analysis.

Cross-validation against historical data

Before relying on any Gann calculator for live analysis, verify it against known historical turning points for the instrument you're trading.

Procedure: 1. Identify 20+ confirmed major turning points in the instrument's history 2. For each turning point, compute the Square of Nine angle (price component) and time projection to the next major turn 3. Check whether the actual next turn fell within ±5% of the projected price level or within ±5 days of the projected date 4. Compute the hit rate

A well-calibrated calculator on a suitable instrument should show hit rates meaningfully above 50% on both price and time projections. If the hit rate is around 40-50%, the calculator's convention is not well-matched to the instrument.

For full backtesting methodology, including how to avoid overfitting this calibration, see our backtesting primer.

Precision vs reliability

Gann calculators give outputs to decimal precision. This precision is a function of arithmetic, not of reliability. A target calculated to the nearest cent doesn't mean the market will reverse to the nearest cent.

Treat Gann price targets as zones, not exact levels. A price target of 105.06 means "watch for resistance in the 104–106 range." Treating it as a limit order level to the pip is misusing the tool.

Similarly, Gann time projections are date windows, not exact days. A projection to March 15 means "watch for a turn in the March 12–20 window." Markets rarely turn on the exact Gann date; they usually turn near it.

See also: Gann Square of Nine 2026 Guide for the broader methodology context.

Related: Gann Square of Nine 2026 Guide | Backtesting Cycle Methods: A Primer