Pie Menu Design

An Empirical Comparison of Pie vs. Linear Menus

An Empirical Comparison of Pie vs. Linear Menus

Jack Callahan, Don Hopkins, Mark Weiser (*) and Ben Shneiderman.
Computer Science Department University of Maryland College Park, Maryland 20742
(*) Computer Science Laboratory, Xerox PARC, Palo Alto, Calif. 94303.
Presented at ACM CHI'88 Conference, Washington DC, 1988.


Pie Menu -vs- Linear Menu Experiment

This is a re-creation in OpenLaszlo of the experiment comparing pie menus and linear menus, described in the paper "A Comparative Analysis of Pie Menu Performance", by Jack Callahan, Don Hopkins, Mark Weiser and Ben Shneiderman. It administers and times the same sequences of pie menus and linear menus as the experiment.

This version measures the selection time and error rate, but doesn't collect or display the information. If I can find the time, I'll extend this to consentually collect usage statistics on the server, and plot graphs of selection time and error rate, as shown in the paper.

The Design and Implementation of Pie Menus -- Dr. Dobb's Journal, Dec. 1991

The Design and Implementation of Pie Menus

There're Fast, Easy, and Self-Revealing.

Copyright (C) 1991 by Don Hopkins.
Originally published in Dr. Dobb's Journal, Dec. 1991, lead cover story, user interface issue.


Although the computer screen is two-dimensional, today most users of windowing environments control their systems with a one-dimensional list of choices -- the standard pull-down or drop-down menus such as those found on Microsoft Windows, Presentation Manager, or the Macintosh.

This article describes an alternative user-interface technique I call "pie" menus, which is two-dimensional, circular, and in many ways easier to use and faster than conventional linear menus. Pie menus also work well with alternative pointing devices such as those found in stylus or pen-based systems. I developed pie menus at the University of Maryland in 1986 and have been studying and improving them over the last five years.

During that time, pie menus have been implemented by myself and my colleagues on four different platforms: X10 with the uwm window manager, SunView, NeWS with the Lite Toolkit, and OpenWindows with the NeWS Toolkit. Fellow researchers have conducted both comparison tests between pie menus and linear menus, and also tests with different kinds of pointing devices, including mice, pens, and trackballs.

Included with this article are relevant code excerpts from the most recent NeWS implementation, written in Sun's object-oriented PostScript dialect.

Instructions for Using Pie Menus - March 1988

How to Choose with Pie Menus
English 393, Technical Writing Assignment #1
Instructions for Performing a Process
Don Hopkins
March 10, 1988

Q: What is the process?
A: The process is selecting from pie menus.

Q: Whis is the audience?
A: The audience is users of the pie menu software for the NeWS window system.

Q: Where would the document be found?
A: It would be part of the documentation that goes along with the software.


Selecting commands from menus is an easy, straightforward way to operate a computer. You can use a pointing device called a "mouse" to indicate the selection you desire, from a list of choices show on the screen. Pie menus (Figure 1) differ from traditional "linear" menus (Figure 2) in the way that their choices are laid out, and the shape of their selection target areas on the screen.

These instructions will describe how to select a choice from a pie menu, cancel a menu without making a selection, and make selections quickly and efficiently.

Pie Menu Cookbook - October 1987

A Pie Menu Cookbook
Techniques for the Design of Circular Menus
By Don Hopkins, October, 1987


Pie menus are used for making selections from items displayed on the computer screen, by pointing and clicking at the desired one with a mouse. The regions of the menu are shaped like the slices of a pie, laid out in a circle around the menu center.

The click of a mouse button invokes a menu, which pops up on the screen positioned so that the cursor is centered in the small inactive region in the menu center. The active target regions are all adjacent to the cursor, but in different directions. Pie menus are fast, because it only takes a small amount of cursor movement to point at one of the regions, and they are accurate, because the wedge shaped regions all have large areas.

The circular layout of pie menus makes them very appropriate for certain tasks. Complementary items can be placed in opposite directions, and spatially oriented items can be put in their appropriate directions. Experienced users can select from familiar pie menus without looking at the menu, and can even mouse ahead into menus faster than the computer can update the screen. When the user selects by mousing ahead into a menu, suppressing the menu display can speed up interaction considerably.

The cursor distance from the menu center can be increased to get more angular precision, for accurate directional selection. It can also be used as an argument to the selection, as a continuous analog value, or a discrete sub-selection.

Users can benefit from commonly used pie menus if they are designed to be easy to learn and use. A window management pie menu with its spatially oriented items in appropriate directions is an example of such a menu. A font selection menu using direction to select font style, and distance to select point size, is an example of how the two-dimensional aspect of pie menus can be exploited.

A user should be able to discern the function of a pie menu by looking at it. A simple, intuitive, consistent look for visually representing the meaning and function of a pie menu can help to create an easy to use user interface. Pie menus can also be designed so that they have a good kinesthetic feel to them, they do not require a lot of wasted mouse movement, and the directions are easier to select, and well matched with the input device.

How Hard Can It Be to Draw a Pie Chart? - October 1987

Date: Tue, 13 Oct 87 00:49:40 EST
From: Don Hopkins <don@brillig.umd.edu>
To: research!td@uunet.uu.net (Tom Duff)
Cc: don@brillig.umd.edu
Subject: Labeling pie graphs is NP hard?

Were you the one who mentioned that someone has found labeling pie graphs to be NP hard, during my pie menu talk at the Usenix Graphics Workshop? If so, or if you know about it, I'd very much appreciate a reference to this work, or a pointer to the person who did it. Thanks a lot.


Eliminating Divides During Pie Menu Tracking - September 1987

Date: Mon, 14 Sep 87 03:03:46 EST
From: Don Hopkins <don@brillig.umd.edu>
To: weiser.pa@xerox.com
Cc: don@brillig.umd.edu
Subject: Eliminating divides during pie menu tracking

Vaughn Pratt suggested an improvement to my quadrant-slope algorythm for pie menu tracking, which eliminates the division done every time the mouse moves during cursor tracking. You can eliminate the divide used to calculate the cursor slope, by multiplying both sides of the slope comparison by the denominator of the cursor slope. i.e. as before, do the divisions to calculate the slopes of the slice edges when laying out the menu. But when tracking the cursor, and comparing its slope with the slice edge slopes, instead of dividing to get the cursor slope, and comparing it with the slice edge slopes, you compare the numerator of the cursor slope with the denominator of the cursor slope times the slice edge slope.

I put the modification into uwm, and it works fine! I want to fix the NeWS pie menus to use this scheme, because they're using atan2 now, and they seem to feel "heavy" when things are going on. Anyway, atan2 loses if you want to have different sized wedges.


Summary of Pie Menus at Usenix Work In Progress Session - June 1987

Directional Selection is Easy as Pie Menus!

Don Hopkins
University of Maryland
Heterogeneous Systems Laboratory
College Park, MD 20742
Written August 1987

Simple Simon popped a Pie Men-
u upon the screen;
With directional selection,
all is peachy keen!

The choices of a Pie Menu are positioned in a circle around the cursor, instead of in a linear row or column. The choice regions are shaped like the slices of a pie. The cursor begins in the center of the menu, in an inactive region that makes no selection. The target areas are all adjacent to the cursor, but in a different directions.

Cursor direction defines the choice. The distance from the menu center to the cursor, because it's independent of the direction, may serve to modify the choice. The further away from the Pie Menu center the cursor is, the more precise the control of the selection is, as the Pie slice widens with distance.

With familiar menus, choices can be made without even seeing the menu, because it's the direction, not the distance, that's important. "Mousing ahead" with Pie Menus is very easy and reliable. Experienced users can make selections quickly enough that it is not actually necessary to display the menu on the screen, if the mouse clicks that would determine the selection are already in the input queue.

The circular arrangement of Pie Menu items is quite appropriate for certain tasks, such as inputing hours, minutes, seconds, angles, and directions. Choices may be placed in intuitive, mnemonic directions, with opposite choices across from each other, orthogonal pairs at right angles, and other appropriate arrangements.

Pie menus have been implemented for uwm, a window manager for X-Windows version 10, for the SunView window system, and for NeWS, Sun's extensible PostScript window system. Don Hopkins did the uwm and NeWS implementations, and Mark Weiser did the SunView implementation.

Jack Callahan has shown Pie Menus to be faster and more reliable than linear menus, in a controlled experiment using subjects with little or no mouse experience. Three types of eight-item menu task groupings were used: Pie tasks (North, NE, East, etc...), linear tasks (First, Second, Third, etc...), and unclassified tasks (Center, Bold, Italic, etc...). Subjects were presented menus in both linear and Pie formats, and told to make a certain selection from each. They were able to make selections 15% faster, with fewer errors, for all three task groupings, using Pie Menus. Ben Shneiderman gave advice on the design of the experiment, and Don Hopkins implemented it in Forth and C, on top of the X-Windows uwm.

Directional Selection is Easy as Pie Menus! - March 1987

Directional Selection is Easy as Pie Menus!
Don Hopkins
University of Maryland
Written March 30, 1987
Abstract for the 4th Usenix Computer Graphics Workshop.

Simple Simon popped a Pie Men-
u upon the screen;
With directional selection,
all is peachy keen!

Pie Menus provide a practical, intuitive, efficient way for people to interact with computers. They run circles around buttoned-down square old pull down menus, in both capability and convenience.

The choices of a Pie Menu are organized in a circle around the cursor, so that the direction of movement makes the choice, allowing the distance to be used in other ways; essentially, they have two outputs: direction and distance. Pie Menus encompass many forms of input: they can utilize various types of hardware, and their two dimensions of output can represent many types of data.

Their circular nature makes them especially well suited for spatially oriented tasks. Menu choices can be positioned in mnemonic directions, with complementary items across from each other, orthogonal pairs at right angles, and other natural arrangements. Pie Menus can make intuitively explicit the symmetry, balance, and opposition between choices.

Choices can be made from Pie Menus in quick, easily remembered strokes. When the direction of a selection in a Pie Menu is known, it can be chosen without even looking. The use of familiar Pie Menus does not require any visual attention, as the use of pull down menus demands.

Experiments comparing pull down menus and Pie Menus have shown clearly that people can choose items faster and with fewer errors from Pie Menus. They are straightforward and simple to master, and facilitate a swift, fluent, natural style of human computer interaction.

Callahan's Pie Menu Versus Linear Menu Experiment - October 1987

Date: Tue, 14 Oct 86 23:28:14 EDT
From: mark@markssun.cs.umd.edu (Mark Weiser)
To: callahan@mimsy.umd.edu, don@mimsy.umd.edu
Subject: pie menus experiments

Jack, I am glad you decided to do a pi menu experiment. I did not read your experimental protocol carefully, but I think it is basically good. I will read it again tomorrow. Experiments are necessary to establish the efficacy of pi menus. If you get your data in time we, you, Don, and I, will have a super pi menu paper.

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