Introducing Numerical Physics (aka Real Physics V2.0) ...

… the App store's only REAL physics simulator, homework solver, and all-round good guy.

Numerical Physics is a touch-based, explicitly numerical, real-time, *point-particle* simulator of Newtonian mechanics in two dimensions for iOS devices, built around a custom physics engine.  It can model, animate and numerically solve with high accuracy a wide class of high school and University mechanics problems you set up yourself using its direct, intuitive touch interface and its open-world 'sandbox' design.

**Numerical Physics PRO is now available: if you need more than a few of the advanced features available through in-app purchase, consider getting the PRO version which has all in-app purchases unlocked (40% savings in USD), and includes a fourth tutorial on some of the advanced features.**

Written by a physicist and educator, designed for educators and students of physics.

Its main main features include the ability to:

· generate dynamically: free-body diagrams, trajectories, and graphs of physical quantities as the system evolves;
· apply a set of standard 'explicit forces' (gravity, drag, spring restoring, inverse square forces);
· constrain bodies to inclines (with or without realistic friction); 
· connect bodies to each other via springs, inverse square law forces, direct tension force constraints, or indirectly through pulley fixed points;
· kinematically constrain (i.e. pre-determine) a body’s motion;
· cause unconstrained and certain singly-constrained bodies to participate in collisions with each other or with a constraint surface, with a user-specified coefficient of restitution, and determine scattering angles and speeds.

Re-written from the ground up Numerical Physics' NEW features include:

· a complete, future-extensible tutorial system: learn physics as you how to use the app;
· a ‘labeled free-body diagram’ view: see, edit, graph and delete your forces right from the FBD;
· an all new UI that gets out of your way and maximizes screen real estate while keeping all features no more than two steps away;
· an all new custom high accuracy, high performance physics engine (10x faster, even higher accuracy);
· an all new OpenGL based graphics engine (100x faster, at a glorious 60 frames/sec even on older hardware);
· server-based examples: so I can post new examples without having to go through an app update;
· universal app design: a single app runs on iPhones of all screen sizes and iPads;
· and last, but not least, the basic app is now free…

Unlock the following features to unleash the full power of the app:

· Advanced Graphing and Data Export: create property vs property, multi-body, and multiple graphs, and export numerical data to apps like spreadsheets;
· Custom Forces and Constraint Curves: create essentially arbitrary position, velocity or time dependent external and interbody forces, and create user-defined ‘non-straight’ constraint curves and surfaces;
· Halter-Solver: specify a 'halting condition' on any physical property of a body that can be graphed: this means that 'Numerical Physics' can be used to numerically solve a wide range of problems commonly encountered in high school through second year University mechanics.
· Multibody and Tension Constraint Solver: create an arbitrary number of bodies (>2), and subject them to as many constraints as is physically consistent. Use it to create powerful simulations of Lagrangian mechanics constrained problems.

Numerical Physics can easily model complex systems numerically that cannot be analytically solved with its choice of five different numerical integrators, time-step, frame rate, and simulation rate control.

What’s New

Version 1.01

- removal of in-app advertising (and associated ad removal IAP)
- bugfixes and memory leak patching/retain cycle removal (Please report crashes to me.)
- UI fixes for custom curve IAP, force graphing
- tutorial fixes
- default to modify body switched to single-tap
- delete OR modify (new) the location of a fixed point/pulley by double tapping on it
- iOS 9 and iPad Pro support

Ratings and Reviews

5.0 out of 5
1 Rating

1 Rating


Kirk Kaminsky
2.7 MB

Requires iOS 9.0 or later. Compatible with iPhone, iPad, and iPod touch.



Age Rating
In-App Purchases
  1. Custom Forces and Constraint Curves $1.99
  2. Advanced Graphing and Data Export $1.99
  3. Multibody and Tension Constraint Solver $1.99


  • Family Sharing

    With Family Sharing set up, up to six family members can use this app.

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