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Ignition Timing (BTDC mm to Degrees)

Convert physical piston drop measurements (millimeters BTDC) directly into exact crankshaft ignition timing degrees using the Law of Cosines.

Engine Geometry

mm
mm
mm

Ignition Timing

19.92 ° BTDC
Crankshaft Angle Before Top Dead Center

Cosine Error Warning

Ensure your dial indicator is perfectly parallel to the cylinder bore axis. If the indicator is tilted (e.g., threading into an angled spark plug hole), the millimeter readings will be artificially inflated by the cosine of the tilt angle, permanently corrupting your timing curve.

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What is The Physics of IgnitionTiming?

The technical foundation and mathematics behind the IgnitionTimingCalc tool.

Mathematical Foundation

Crankshaft Angle via Law of Cosines
θ=arccos⁡(x2+r2−R22xr)\theta = \arccos\left(\frac{x^2 + r^2 - R^2}{2xr}\right)
θ\theta= Resulting Crankshaft Angle Before Top Dead Center (BTDC) in Radians.
xx= Calculated distance from the center of the crank to the dropped piston pin (TDC Height - Piston Drop) (mm).
rr= Crankshaft Throw Radius (Engine Stroke ÷ 2) (mm).
RR= Connecting Rod absolute length from center to center (mm).

Laws & Principles

  • Geometric Limits: The piston cannot physically drop further from Top Dead Center than the total Engine Stroke. Any measurement exceeding the stroke is physically impossible and indicates tool slippage.
  • The Dial Indicator Trajectory Warning: This exact mathematical geometry assumes your dial indicator is perfectly parallel with the vertical bore of the cylinder. If you thread the indicator into an offset, angled spark-plug hole (common on dome-chamber 4-strokes), all dial readings will be artificially inflated by the internal cosine of the hole's tilt angle, completely crashing the timing map.

Step-by-Step Example Walkthrough

" A mechanic has measured exactly 2.0mm of physical piston drop on a 54mm stroke racing engine equipped with a 110mm swept connecting rod. "

  1. 1. Find the Crank Radius (r): 54 / 2 = 27.0mm.
  2. 2. Find the absolute physical height distance at true TDC: Rod (110) + Crank Radius (27) = 137.0mm.
  3. 3. Determine the structural height at the dial indicator's dropped position: 137.0 - 2.0mm drop = 135.0mm (x vector).
  4. 4. Apply the Law of Cosines: (135² + 27² - 110²) / (2 × 135 × 27).
  5. 5. The matrix yields the raw cosine value representing the angle of the crankshaft arm relative to the vertical cylinder bore axis.
  6. 6. Take the arc-cosine of that fractional value and mathematically convert the resulting radians back to structural degrees.
Final Result: The engine is currently timed to fire at exactly 19.34 Degrees Before Top Dead Center (BTDC).

Quick Answer: Why Convert mm BTDC to Degrees?

Most racing 2-strokes are manually timed by measuring how far the piston physically drops in the cylinder Before Top Dead Center (BTDC) using a dial indicator. However, if you are upgrading from an older mechanical stator to a modern programmable Electronic Control Unit (ECU), the ECU software requires the ignition map to be entered exclusively in Rotational Degrees. You cannot type "2.0mm" into a MoTeC or Zeeltronic ECU. Because piston travel speed completely changes depending on the engine's stroke and connecting rod length, you cannot use a generic conversion chart. Use the Ignition Timing (BTDC mm to Degrees) Calculator above to mathematically apply the Law of Cosines to your specific engine geometry, converting your physical dial indicator measurement directly into a perfect degree value for your engine management software.

Timing Mapping Failures

The Google Chart Disaster

An amateur builder installs a programmable CDI on their modified Yamaha Banshee 350. They know the engine ran best on the mechanical stator when dialed to exactly 2.0mm BTDC. They Google "2.0mm to degrees" and click the first generic chart they find, which says 2.0mm equals 17°. They program 17° across the entire ECU map. Unfortunately, that chart was specifically calculated for a long-rod 250cc motocross bike. Because the Banshee has a shorter 54mm stroke, 2.0mm actually equates to over 21° of advance. The engine is massively over-advanced for the fuel being used, resulting in severe pre-ignition that shatters both ring lands on the first dyno pull.

The EFI Conversion Win

A technician is retrofitting Electronic Fuel Injection (EFI) onto a vintage 100cc air-cooled kart engine. The engine builder provides the timing specs strictly in millimeters, stating: "Idle at 1.8mm, peak torque at 2.4mm, roll off to 1.5mm at max RPM." To build the 3D ignition map in the new Haltech ECU, the technician uses the calculator, inputting the kart's 50mm stroke and 95mm rod. They convert the three required mm drops into perfect degrees (19.6°, 23.0°, 17.8°). The resulting ECU map perfectly mimics the physical magneto curve, allowing the engine to start flawlessly while gaining all the benefits of electronic tuning.

Typical ECU Base Map Timings (Degrees BTDC)

Operating State Typical Spark Advance Primary Tuning Goal
Cranking / Starting0° - 5° BTDCPrevent violent starter kick-back
Low RPM Idle10° - 15° BTDCMaintain stable, smooth rotation
Peak Engine Torque20° - 28° BTDCMaximum cylinder combustion pressure
Peak High RPM (Over-Rev)14° - 8° BTDCRetard timing to shift heat into exhaust pipe

Note: A programmable ECU allows you to build a dynamic curve. You generally advance the timing heavily to hit peak torque in the mid-range, and then purposely retard the timing (lower the degrees) at maximum RPM. Retarding the timing at redline dumps excess heat into the expansion chamber, which physically alters the speed of sound and forces the pipe's acoustic powerband to rev even higher.

Pro Tips for Degree Conversions

Do This

  • ✓Use Center-to-Center rod measurements. When inputting the Connecting Rod Length into the calculator, it must be the absolute measurement from the exact center of the big-end bearing to the exact center of the small-end wrist pin bearing. Do not measure the total outer length of the rod itself.
  • ✓Account for spark plug angle. If your dial indicator inserts into the cylinder head at an angle (common on hemi-heads), the true vertical mm drop gets artificially extended by the cosine of that angle. You must mathematically correct your dial reading to true vertical mm before inputting it into this calculator to find accurate degrees.

Avoid This

  • ✗Don't guess the stroke geometry. If you bore out a cylinder, the stroke remains identical. However, if you install an aftermarket "stroker crank" (e.g., changing from a 54mm to a 58mm stroke), your entire timing math instantly changes. You must recalculate the degree conversion using the new 58mm value.
  • ✗Don't confuse BTDC with ATDC. This calculator strictly measures Before Top Dead Center. If you rotate the engine the wrong direction when dropping the piston from TDC, you will calculate degrees for After Top Dead Center. Firing the spark plug at 20° ATDC will cause the combustion to chase the piston down the bore, generating zero power and massive exhaust heat.

Frequently Asked Questions

Why isn't 2.0mm piston drop the same degrees on every engine?

Because piston travel near Top Dead Center is controlled by the connecting rod swinging outward in an arc. An engine with a massively long stroke and a short connecting rod creates a highly aggressive rod angle, causing the piston to dwell near TDC longer before accelerating downward extremely fast. This completely breaks any linear conversion scale.

Do I need this calculator if I have a timing light?

No. If your engine flywheel already has distinct factory degree lines stamped into the metal, and you have an optical timing light, you can visually verify the timing degrees while the engine is running. This calculator is strictly required for engines that lack external degree marks, forcing you to mathematically convert physical piston drop into degrees.

Does piston dome shape affect this calculation?

No. Whether the piston is perfectly flat, domed, or dished, the total vertical mechanical drop from its own absolute peak (TDC) remains identical. The dial indicator measures relative vertical displacement, which depends entirely on crank and rod geometry, not the shape of the surface being touched.

What does "Law of Cosines" mean in this context?

The engine's crankshaft radius, connecting rod, and vertical cylinder bore form a constantly shifting triangle. The Law of Cosines is the fundamental trigonometric formula that allows us to find the unknown top angle (the crankshaft rotational degrees) if we know the physical lengths of the three mechanical sides (Radius, Rod, and Piston Height).

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