Meeting the Pianist’s Expectations: The Grand Piano Action Ratio
Whether or not you realize it, when you approach a piano, you have certain expectations. For example, you expect the key to depress 10mm. While small variations (under 1mm) are likely to go unnoticed, much beyond that and something will start to feel “off”. Harpsichord keys for instance, only travel around 5-7mm and this is often one of the first things piano players notice. Piano technicians refer to the travel of the front of the key as key dip.
Of course, this is not your only expectation. You also expect the hammer to strike the strings at a certain moment in the key stroke. That is typically around 8.5mm into the 10mm key dip. The remaining 1.5mm of key travel after the hammer strikes the strings allows room for the parts to cycle, and quickly reset without interfering with each other when the key is released. Piano technicians refer to the key travel after the hammer strikes the strings as aftertouch.
| Term | Definition | Pianist’s Expected Value |
|---|---|---|
| Key Dip | The total vertical distance the front of the key travels when played. | 10mm |
| Aftertouch | The vertical distance the front of the key travels after the hammer strikes the strings. | 1.25-1.5mm |
The key is only one side of the equation: the input. On the other end is the hammer: the output. In order to gain enough momentum for maximum power, the hammer typically must travel around 45mm (±2mm) before striking the strings. Piano technicians refer to the travel of the hammer as blow distance.
When you press a key, a piece called the jack forces the hammer toward the strings (see Video 1). To keep the hammer from blocking into the strings, there must be a moment when the jack stops forcing the hammer upward. This typically occurs when the hammer is around 2mm from the strings. At this moment, the jack stops contacting the hammer assembly. The hammer then travels the rest of the way to the strings due to momentum. Less momentum produces a softer sound. More momentum results in a louder sound. Thus the piano can play forte (loud) or piano (soft) and everything in between based solely on how hard the pianist presses the key. Fun fact: the original name for the piano was “clavicembalo col piano e forte,” which translates roughly to “the harpsichord that can play loud and soft”. Today we refer to these early instruments as fortepianos (or “loud/softs”). With time, the forte was removed and the instrument is now known simply as the piano.
Video 1: The jack slowly pushing the hammer until it is ~2mm from the strings.
Piano technicians refer to the moment the jack ceases contact with the hammer assembly as let-off.
| Term | Definition | Pianist’s Expected Value |
|---|---|---|
| Blow Distance | The total vertical distance the hammer travels from its rest position to the strings. | 45mm (±2) |
| Let-off | The distance from the top of the hammer to the strings when the jack stops moving the hammer upward. | 1.5-2mm |
In order to meet the expectations of the pianist, the piano action (its moving parts) must be designed with the necessary ratio to produce these expected results. For example, if the input (key dip) needs to be 10mm and the output (blow distance) needs to be 45mm, then the resulting ratio (output/input) would need to be 4.5:1. Meaning that for every millimeter the key travels, the hammer moves 4.5mm.
It is not quite that simple. This is because the actual input the pianist can control is from the start of the key dip until the hammer strikes the strings. In other words, key dip minus aftertouch. So in reality the pianist’s input is actually 8.5mm (10mm of key dip - 1.5mm of aftertouch).
The same is true for the hammer. While the overall blow distance may be 45mm, the pianist only controls that distance until the jack stops moving the hammer upward. In other words, blow distance minus let-off. So in reality the pianist’s output is actually 43mm (45mm of blow distance minus 2mm of let-off).
Thus the true action ratio (output/input) is 5.06:1. Meaning that for every millimeter the key travels, the hammer travels 5.06mm. Admittedly, even this is an oversimplification because the parts don’t move straight up and down, but in arcs. This means that the action ratio changes through the key stroke. Starting higher (perhaps 5.5:1) then reducing until the moment of let-off, which is also called the moment of escapement. At the moment of escapement, the ratio of a modern piano action should be very close to 5:1.
This overall action ratio is actually the result of three ratios. The piano action is made up of three levers, each with its own input and output. These are 1) the key, 2) the hammer assembly, and 3) the wippen assembly. The wippen is the piece that connects the key motion to the hammer via the jack. Each lever is measured between a point of contact to a point of rotation.
The key input is measured from the front of the key (the hypothetical point of contact with the pianist) to the center of the hole on the bottom of the key. This is where the key pivots (point of rotation). See Image 1.
Image 1: Measuring Key Input.
The key output is measured as the distance from the center of the hole on the bottom of the key (point of rotation) to the center of the top of the capstan. The capstan is the brass piece on the back of the key that contacts the wippen assembly (point of contact). See Image 2.
Image 2: Measuring Key Output.
The wippen input is measured as the distance from the bottom of the wippen at the spot that rests on the capstan (point of contact with the key) to the wippen flange center pin (point of rotation). See Image 3.
Image 3: Measuring Wippen Input.
The wippen output is measured as the distance from the wippen flange center pin (point of rotation) to the rear top edge of the jack (point of contact with the hammer assembly). See Image 4.
Image 4: Measuring Wippen Output.
The hammer input is measured as the distance from the bottom of the knuckle (point of contact with the wippen assembly) to the hammer flange center pin (point of rotation). The knuckle is the part of the hammer assembly that the jack pushes to force the hammer upward.
In Image 5, I am actually measuring the distance between the center of the wood knuckle core and the hammer flange center pin.
Image 5: Measuring Hammer Input.
This is because the hammer input is difficult to measure accurately. Instead, we can measure the distance from the hammer flange center pin to the center of the knuckle core and input the following values as listed below:
If the knuckle is 15.5mm from the hammer flange center pin, then hammer input = 20.2mm
If the knuckle is 16.2mm from the hammer flange center pin, then hammer Input = 20.8mm
If the knuckle is 17mm from the hammer flange center pin, then hammer input = 21.4mm
These numbers were calculated using basic trigonometry as shown in Image 6.
Image 6: Calculating Hammer Input. Diagram Courtesy of Nick Gravagne, RPT.
The numbers above assume that the diameter of the knuckle is 10mm. If the hammer assembly has a 9.5mm knuckle, then you could subtract 0.30mm from the values above.
Finally, the hammer output is measured as the distance from the hammer flange center pin (point of rotation) to the top center of the hammer (point of contact with the strings). See Image 7.
Image 7: Measuring Hammer Output.
Thus, all of the inputs and outputs are shown together in Image 8.
Image 8: The Three Levers of the Grand Piano Action.
With these measurements in hand, you can calculate the action ratio using the following formula.
The results from Formula #2 should be similar to those from Formula #1. For modern action parts, the overall action ratio should be around (4.9-5.3):1. Otherwise, the pianist’s expectations will not be met.
If you purchase a new grand piano today, then this action ratio is a standard feature, but it wasn’t always this way. Steinway, for example, used to manufacture their pianos with a much higher action ratio than what they use today. In the Piano Technology Shop in the Music Building at Brigham Young University, we are constantly rebuilding the grand pianos in the School of Music Inventory. On some older pianos, this also means redesigning their actions to meet modern standards and expectations. For example, some of our piano inventory dates back to before the Harris Fine Arts Center and all of those actions have been completely modernized. We also have a Steinway in our shop right now from the late 1890s. To satisfy the pianists in the School of Music, we will likely need to order action parts that adjust the inputs and outputs of the hammer or wippen assemblies so that a 5:1 ratio can be achieved. We might also consider relocating the capstan on the back of the keys until the overall action ratio is what modern pianists have come to expect. Knowledge can unlock the power of a great design!
To cite this article:
Cassel, Jason. “Meeting the Pianist’s Expectations: The Grand Piano Action Ratio.” The BYU Design Review, 25 May 2026, https://www.designreview.byu.edu/collections/meeting-the-pianists-expectations-the-grand-piano-action-ratio.
