← Back to article

Equation 1 · Why Claude Code Delegates to Subagents, and What That Actually Buys You

What does this equation mean?

Ttotal=Tparent+∑i=1kTsubagenti,Tparent≪∑i=1kTsubagenti.T_{\mathrm{total}} = T_{\mathrm{parent}} + \sum_{i=1}^{k} T_{\mathrm{subagent}_i}, \qquad T_{\mathrm{parent}} \ll \sum_{i=1}^{k} T_{\mathrm{subagent}_i}.

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

TtotalT_{\mathrm{total}}

Symbol T_total

TtT_total is part of the quantity the equation computes from the expression on the right.

Understand this part →

TparentT_{\mathrm{parent}}

Symbol T_parent

TpT_parent is one of the signed contributions combined to compute the quantity on the left.

Understand this part →

ii

Symbol i

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Understand this part →

kk

Symbol k

k appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Understand this part →

TsubagentiT_{\mathrm{subagent}_i}

Symbol T_subagent_i

TsT_subagentit_i is one of the signed contributions combined to compute the quantity on the left.

Understand this part →

=

=

The expressions on both sides represent the same quantity under the stated assumptions.

Understand this part →

See an illustrated explanation →
addition

addition

Add the term after the plus sign to the term or group before it.

Understand this part →

subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Understand this part →

superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Understand this part →

See an illustrated explanation →
i=1i=1

Starting index or lower bound: i=1

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Understand this part →

kk

Ending index or upper bound: k

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

Understand this part →

i=1i=1

Starting index or lower bound: i=1

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Understand this part →

kk

Ending index or upper bound: k

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

Understand this part →

How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

This is the specific problem a subagent is built to solve, and Claude Code’s own documentation gives a concrete, numeric illustration of the effect rather than an abstract claim about it. In a worked session example, a subagent delegated to research a piece of session-timeout handling reads three files totalling 6,100 tokens of raw source, entirely inside its own isolated window — “None of this touches your main context,” the documentation notes of the reads — and returns a single 420-token summary to the parent conversation, which the documentation flags directly: “That’s the context savings” [ 2 ] . The parent’s window absorbs an addition roughly a fourteenth the size of what was actually…
Read the full surrounding passage
This is the specific problem a subagent is built to solve, and Claude Code’s own documentation gives a concrete, numeric illustration of the effect rather than an abstract claim about it. In a worked session example, a subagent delegated to research a piece of session-timeout handling reads three files totalling 6,100 tokens of raw source, entirely inside its own isolated window — “None of this touches your main context,” the documentation notes of the reads — and returns a single 420-token summary to the parent conversation, which the documentation flags directly: “That’s the context savings” [ 2 ] . The parent’s window absorbs an addition roughly a fourteenth the size of what was actually read. Put as a simple accounting identity, isolation does not shrink the total amount of computation a system performs; it relocates where that computation’s output lands: Ttotal=Tparent+∑i=1kTsubagenti,Tparent≪∑i=1kTsubagentiT_{\mathrm{total}} = T_{\mathrm{parent}} + \sum_{i=1}^{k} T_{\mathrm{subagent}_i}, \qquad T_{\mathrm{parent}} \ll \sum_{i=1}^{k} T_{\mathrm{subagent}_i}. The parent conversation’s occupied share of its own window, TparentT_{\mathrm{parent}} , stays small and bounded even as the total work performed across k delegated subagents grows without bound. That inequality is the real content behind the phrase “context savings” — the saving is measured in the one window that has to keep attending to everything else in the task, not in total tokens billed.

Read the equation in its article →

Sources cited in the surrounding passage

These citations give research context. Read each source to check which claims it supports.

Return to Why Claude Code Delegates to Subagents, and What That Actually Buys You

See this formula across 1 published context →

Browse the mathematical compendium →