Calculate injector end angle (EOI) from start of injection, pulse width, and engine speed. Get wrapped 0–720° EOI, injection duration in degrees, and 4-stroke duty cycle.
Formulas & Conventions
This calculator uses a standard absolute crank angle progression (End Angle = Start Angle + Duration Angle). Results are mathematically wrapped within a standard 0-720° engine cycle.
Duration Angle Formula:
Duration (°) = Pulse Width (ms) × RPM × 0.006
End of Injection (EOI):
EOI (°) = (SOI + Duration) % 720
Duty Cycle Assumption:
The duty cycle percentage explicitly assumes standard 4-stroke engine operation (720° per full cycle).
Getting your engine’s fuel delivery mapped correctly requires translating time-based injector commands into crankshaft rotation. Our injector end angle calculator helps you find the calculated point in the engine cycle where fuel injection stops mathematically, known as the End of Injection (EOI). It takes your engine speed, start angle, and pulse width to map out your injection duration in degrees and your overall injector duty cycle.
What Is Injector End Angle
The injector end angle, or End of Injection (EOI), is the crank angle degree at which the fuel injector finishes its commanded fuel delivery. In a standard 4-stroke engine, a complete cycle takes 720 degrees of crankshaft rotation.
When the Engine Control Unit (ECU) triggers the injector to open, that is the Start of Injection (SOI). The time the injector remains energized is the Pulse Width (PW), measured in milliseconds. As the engine spins, that time translates into a specific number of crankshaft degrees.
It is important to understand how your specific ECU references this starting angle. While this calculator uses an absolute 0-720 degree timeline, different ECUs might reference SOI relative to Top Dead Center (BTDC/ATDC), specific stroke events (like intake or compression), or a proprietary trigger wheel offset. You will need to normalize your ECU’s start angle to a standard absolute degree value to accurately use this tool.
Additionally, be aware that some data loggers or systems may display duty cycle against different reference windows or timebases. Always ensure you match your specific ECU or logger convention before comparing these values directly across platforms.
Why Calculate End Of Injection
Converting time into degrees is a critical part of understanding your fuel system’s physical limits. It is important to state that this tool is a kinematic angle converter, not a combustion optimizer. It mathematically calculates where the injection event ends based on time and RPM, but it does not tell you if that timing is optimal for your specific cam timing, valve overlap, or injector placement.
Tuners calculate the EOI to visualize the injection window. By knowing the calculated duration in degrees, you can see if your injector is open for too much of the 720-degree cycle. If your calculated duration is extremely long, the EOI pushes further into the engine cycle, giving you a clear mathematical picture of how heavily your fuel system is being taxed.
While the duty cycle shows the consequences of your setup, remember that this tool does not determine absolute injector sizing by itself; it simply prevents you from reading timing conclusions too literally without understanding the limits. It helps bridge the gap between the milliseconds logged in your tuning software and the physical rotation of the engine.
Formula / How It Is Calculated
The tool uses standard engine kinematics to convert time-based millisecond measurements into rotation-based degrees. The entire calculation revolves around a standard 4-stroke 720-degree engine cycle.
First, the calculator converts your injection pulse width into crankshaft rotation degrees based on your current engine speed:$$\text{Duration} (^\circ) = \text{PW} \times \text{RPM} \times 0.006$$
Next, to find the raw angle where the injection ends, it adds this duration to your starting angle:$$\text{Raw EOI} (^\circ) = \text{SOI} + \text{Duration}$$
Because engine cycles repeat, the formula uses a modulo operation (represented by mod 720) to wrap the result within a standard engine cycle.$$\text{Wrapped EOI} (^\circ) = (\text{SOI} + \text{Duration}) \pmod{720}$$
Finally, the tool calculates the injector duty cycle, showing what percentage of the available 4-stroke cycle the injector spends open:$$\text{Duty Cycle} (\%) = \frac{\text{PW} \times \text{RPM}}{1200}$$
Examples Of Injector Timing
Suppose you are tuning a 4-stroke engine and need to verify the mathematical window of your fuel delivery at high RPM. You know your engine is running at 6000 RPM. Your ECU is commanding a Start of Injection (SOI) at an absolute angle of 0 degrees, and the current injection pulse width (PW) logged by the ECU is 12.5 milliseconds. You wish to measure the End of Injection (EOI) and the total duration in degrees.
You now have all the relevant information needed for the programme. Go to the input fields on the tool. Enter 6000 for the Engine Speed, hit the tab key then enter 0 for the Start of Injection (SOI), hit the tab key again and enter 12.5 for the Injection Duration (PW). The tool automatically reads these inputs as you type. The answers are then calculated instantly: an End of Injection (EOI) of 450.0 degrees, a total injection duration of 450.0 degrees, and an injector duty cycle of 62.5%.
Suppose you push the engine harder, reaching 8500 RPM with a heavy fuel load requiring a 16.0 ms pulse width, starting at 0 degrees. You enter 8500 for RPM, 0 for SOI, and 16.0 for PW. The tool calculates a duration of 816.0 degrees. Because this duration exceeds a full engine cycle, the raw angle (816 degrees) wraps around the 720-degree mark, resulting in a displayed EOI of 96.0 degrees.
Furthermore, the duty cycle calculates to 113.3%. This instantly tells you that the commanded fueling is physically impossible, as the injector is being asked to stay open longer than the engine cycle itself.
Reference Table For Injection Duration Limits
To understand how engine speed changes crankshaft rotation during a fixed amount of time, review this table. It shows how a static 15.0 ms injection pulse width behaves as RPM climbs, eventually leading to cycle overrun.
| Engine Speed (RPM) | Pulse Width (ms) | Duration in Degrees (°) | Duty Cycle (%) | Status |
|---|---|---|---|---|
| 3000 | 15.0 | 270.0° | 37.5% | Normal |
| 5000 | 15.0 | 450.0° | 62.5% | Normal |
| 7000 | 15.0 | 630.0° | 87.5% | Heavy Load |
| 8000 | 15.0 | 720.0° | 100.0% | Static (Fully Open) |
| 9000 | 15.0 | 810.0° | 112.5% | Cycle Overrun |
Using The Injector End Angle Calculator
This tool is designed to give you instant conversions from time-based ECU data to absolute crank degrees without manually doing the math.
To get accurate results, ensure your Engine Speed (RPM) is a positive number. Your Start of Injection (SOI) must be entered as an absolute crank angle degree. Since ECUs vary greatly in how they define 0 degrees (some use TDC compression, others use trigger wheel sync points), make sure you normalize your ECU’s starting angle to standard absolute degrees before inputting it. The Injection Duration (PW) is the time the injector is energized, measured in milliseconds.
The results panel will display both the raw, unwrapped End of Injection (EOI) and the wrapped value between 0 and 720 degrees. It also breaks out the pure Duration angle, showing how many degrees of rotation the engine covers while the injector is open. Pay close attention to the Duty Cycle percentage.
The calculator will output the raw mathematical duty cycle based on your inputs. If you see a number over 100%, or a duration over 720 degrees, the calculator will flag this with a warning message, as you have exceeded the physical limits of the engine cycle.
Frequently Asked Questions
Why is my duty cycle over 100%?
If the calculator returns a duty cycle over 100%, it means the time required to inject the fuel (Pulse Width) is longer than the time it takes the engine to complete a full 720-degree rotation at that RPM. Physically, the injector would be “static” (open continuously) and still fail to deliver the requested fuel within the cycle. This usually indicates that larger fuel injectors or higher fuel pressure are required.
What does a wrapped EOI mean if my duration is over 720 degrees?
Because a 4-stroke cycle resets every 720 degrees, the calculator uses modulo math to wrap the final EOI back into the 0-720 window. However, if your pure Duration is greater than 720 degrees (cycle overrun), the displayed EOI represents where the injector stops in the next engine cycle.
Seeing the Raw EOI helps prevent confusion here. The wrapping math is correct, but functionally, an overrun means your injector is overlapping across cycles and is constantly open.What is considered a safe injector duty cycle?
While the calculator will run the math for any input, general aftermarket tuning guidance suggests keeping maximum duty cycles around 80% to 85%. This is not a strict universal engineering law, but leaving a 15-20% margin allows adequate time for the injector coil to discharge and the mechanical pintle to physically close and recover before the next cycle begins.
Does this tool tell me the best injection timing?
No. This calculator is strictly a kinematic tool. It mathematically maps the time-based injection event onto the degree-based crankshaft rotation. It does not account for valve events, cam timing, or intake port geometry, meaning it cannot determine whether your calculated EOI is optimal for atomization or performance.
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